Word Problems - ACT Math
Card 1 of 30
What is the first step in solving a time, rate, and distance problem?
What is the first step in solving a time, rate, and distance problem?
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Identify given values for time, rate, or distance. Organize known information before applying $d = rt$ formula.
Identify given values for time, rate, or distance. Organize known information before applying $d = rt$ formula.
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What does the phrase "per" usually indicate in an ACT word problem expression?
What does the phrase "per" usually indicate in an ACT word problem expression?
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"Per" usually means division, as in $60$ miles per $2$ hours is $\frac{60}{2}$. This indicates division to find rate in word problems.
"Per" usually means division, as in $60$ miles per $2$ hours is $\frac{60}{2}$. This indicates division to find rate in word problems.
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Identify the translation: "three times the sum of $x$ and $4$" becomes what expression?
Identify the translation: "three times the sum of $x$ and $4$" becomes what expression?
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$3(x+4)$. First add $x$ and 4, then multiply by 3.
$3(x+4)$. First add $x$ and 4, then multiply by 3.
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What does the phrase "of" usually indicate in an ACT word problem expression?
What does the phrase "of" usually indicate in an ACT word problem expression?
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"Of" usually means multiplication, as in $\frac{3}{4}$ of $x$ is $\frac{3}{4}x$. This indicates multiplication in word problems.
"Of" usually means multiplication, as in $\frac{3}{4}$ of $x$ is $\frac{3}{4}x$. This indicates multiplication in word problems.
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What is the work-rate equation for two workers with rates $r_1$ and $r_2$ working together?
What is the work-rate equation for two workers with rates $r_1$ and $r_2$ working together?
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$r_1+r_2=r_{\text{total}}$. Combined work rates add when working together.
$r_1+r_2=r_{\text{total}}$. Combined work rates add when working together.
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Identify the translation: "the difference of $x$ and $4$" becomes what expression?
Identify the translation: "the difference of $x$ and $4$" becomes what expression?
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$x-4$. Subtract the second number from the first.
$x-4$. Subtract the second number from the first.
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Identify the translation: "the quotient of $x$ and $5$" becomes what expression?
Identify the translation: "the quotient of $x$ and $5$" becomes what expression?
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$\frac{x}{5}$. Divide the first number by the second.
$\frac{x}{5}$. Divide the first number by the second.
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If $15$ is $25%$ of $x$, what is $x$?
If $15$ is $25%$ of $x$, what is $x$?
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$60$. $15 = 0.25x$, so $x = 60$
$60$. $15 = 0.25x$, so $x = 60$
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A price increases from $50$ to $60$ dollars; what is the percent increase?
A price increases from $50$ to $60$ dollars; what is the percent increase?
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$20%$. $\frac{60-50}{50} \times 100% = 20%$
$20%$. $\frac{60-50}{50} \times 100% = 20%$
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Two cars start $300$ miles apart and drive toward each other at $60$ mph and $40$ mph; when do they meet?
Two cars start $300$ miles apart and drive toward each other at $60$ mph and $40$ mph; when do they meet?
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$3$ hours. Combined speed is $100$ mph, so $\frac{300}{100} = 3$ hours.
$3$ hours. Combined speed is $100$ mph, so $\frac{300}{100} = 3$ hours.
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A fair coin is flipped twice; what is the probability of exactly one head?
A fair coin is flipped twice; what is the probability of exactly one head?
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$\frac{1}{2}$. Two outcomes (HT, TH) out of four possible.
$\frac{1}{2}$. Two outcomes (HT, TH) out of four possible.
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A jar has $5$ red and $3$ blue marbles; what is the probability of drawing a red marble?
A jar has $5$ red and $3$ blue marbles; what is the probability of drawing a red marble?
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$\frac{5}{8}$. 5 red out of 8 total marbles.
$\frac{5}{8}$. 5 red out of 8 total marbles.
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Find the total cost if 5 items cost $x$ each and a $20 fee is added.
Find the total cost if 5 items cost $x$ each and a $20 fee is added.
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Total Cost = $5x + 20$. Multiplies unit cost by quantity, then adds fixed fee.
Total Cost = $5x + 20$. Multiplies unit cost by quantity, then adds fixed fee.
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What equation represents 'Four times a number is reduced by 8 to get 16'?
What equation represents 'Four times a number is reduced by 8 to get 16'?
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Equation: $4x - 8 = 16$. Translates 'reduced by 8' as subtraction from $4x$.
Equation: $4x - 8 = 16$. Translates 'reduced by 8' as subtraction from $4x$.
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Identify the equation for 'Three times a number equals 18.'
Identify the equation for 'Three times a number equals 18.'
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Equation: $3x = 18$. Direct translation of 'three times' as multiplication.
Equation: $3x = 18$. Direct translation of 'three times' as multiplication.
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What is the equation for 'A number is divided by 4 to give 3'?
What is the equation for 'A number is divided by 4 to give 3'?
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Equation: $\frac{x}{4} = 3$. Translates division phrase into fractional equation.
Equation: $\frac{x}{4} = 3$. Translates division phrase into fractional equation.
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How do you set up a system of equations for a word problem?
How do you set up a system of equations for a word problem?
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Translate conditions into algebraic equations. Convert word relationships into mathematical expressions.
Translate conditions into algebraic equations. Convert word relationships into mathematical expressions.
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How do you express consecutive odd numbers algebraically?
How do you express consecutive odd numbers algebraically?
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Use $x, x+2, x+4, \text{etc.}$. Odd numbers differ by 2, starting from any odd $x$.
Use $x, x+2, x+4, \text{etc.}$. Odd numbers differ by 2, starting from any odd $x$.
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Identify the equation for 'The sum of a number and 9 is 15.'
Identify the equation for 'The sum of a number and 9 is 15.'
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Equation: $x + 9 = 15$. Direct translation of 'sum' as addition operation.
Equation: $x + 9 = 15$. Direct translation of 'sum' as addition operation.
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Express 'The difference between a number and 6 is 8' as an equation.
Express 'The difference between a number and 6 is 8' as an equation.
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Equation: $x - 6 = 8$. Translates 'difference' as subtraction operation.
Equation: $x - 6 = 8$. Translates 'difference' as subtraction operation.
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What is the first step in solving a time, rate, and distance problem?
What is the first step in solving a time, rate, and distance problem?
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Identify given values for time, rate, or distance. Organize known information before applying $d = rt$ formula.
Identify given values for time, rate, or distance. Organize known information before applying $d = rt$ formula.
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How do you calculate the selling price with a discount?
How do you calculate the selling price with a discount?
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Selling Price = Original Price × (1 - Discount Rate). Multiplies by $(1 - \text{decimal discount})$ to reduce price.
Selling Price = Original Price × (1 - Discount Rate). Multiplies by $(1 - \text{decimal discount})$ to reduce price.
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Express 'The product of a number and 7 is 21' as an equation.
Express 'The product of a number and 7 is 21' as an equation.
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Equation: $7x = 21$. Translates 'product of number and 7' directly as multiplication.
Equation: $7x = 21$. Translates 'product of number and 7' directly as multiplication.
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What equation represents 'Four more than twice a number is 10'?
What equation represents 'Four more than twice a number is 10'?
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Equation: $2x + 4 = 10$. Translates 'twice a number' as $2x$ and 'four more' as $+4$.
Equation: $2x + 4 = 10$. Translates 'twice a number' as $2x$ and 'four more' as $+4$.
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What equation represents 'Three times a number decreased by 4 equals 11'?
What equation represents 'Three times a number decreased by 4 equals 11'?
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Equation: $3x - 4 = 11$. Translates 'three times' as $3x$ and 'decreased by 4' as $-4$.
Equation: $3x - 4 = 11$. Translates 'three times' as $3x$ and 'decreased by 4' as $-4$.
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What is the equation for a simple interest word problem?
What is the equation for a simple interest word problem?
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Interest = Principal × Rate × Time. Standard formula for calculating simple interest earned.
Interest = Principal × Rate × Time. Standard formula for calculating simple interest earned.
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What is the key step in solving mixture word problems?
What is the key step in solving mixture word problems?
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Set up an equation based on total quantity or concentration. Balance total amounts or percentages to find unknowns.
Set up an equation based on total quantity or concentration. Balance total amounts or percentages to find unknowns.
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How do you solve a percent decrease word problem?
How do you solve a percent decrease word problem?
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New Value = Original Value × (1 - Percent Decrease). Multiplies by $(1 - \text{decimal percent})$ for decrease.
New Value = Original Value × (1 - Percent Decrease). Multiplies by $(1 - \text{decimal percent})$ for decrease.
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Find the equation: 'Twice a number added to 3 equals 11.'
Find the equation: 'Twice a number added to 3 equals 11.'
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Equation: $2x + 3 = 11$. Translates 'twice a number added to 3' as $2x + 3$.
Equation: $2x + 3 = 11$. Translates 'twice a number added to 3' as $2x + 3$.
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State the method to find an unknown in a ratio problem.
State the method to find an unknown in a ratio problem.
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Use cross-multiplication to solve the proportion. Cross-multiplication solves proportional equations efficiently.
Use cross-multiplication to solve the proportion. Cross-multiplication solves proportional equations efficiently.
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