ISEE Middle Level Mathematics Achievement Flashcards: Equation From A Situation

What this deck covers

This deck focuses on Equation From A Situation, giving you a quick way to review the definitions, rules, and examples that matter most for ISEE Middle Level Mathematics Achievement.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: Which equation models: You buy $x$ notebooks at $3 each and pay $2 tax; total cost is $T$?

Answer: $T=3x+2$. Calculates total cost as the price per notebook times quantity plus fixed tax.

Flashcard 2: Which equation models: A car starts with $g$ gallons and uses $0.05$ gallons per mile for $x$ miles; remaining gas is $R$?

Answer: $R=g-0.05x$. Subtracts the gas consumed at 0.05 gallons per mile from the initial amount.

Flashcard 3: Which equation models: The sum of two consecutive integers is $41$; let the first be $n$?

Answer: $n+(n+1)=41$. Adds two consecutive integers to equal 41.

Flashcard 4: Which equation models: The sum of three consecutive integers is $72$; let the middle integer be $n$?

Answer: $(n-1)+n+(n+1)=72$. Sums three consecutive integers with n as the middle to equal 72.

Flashcard 5: Which equation models: A rectangle has width $w$ and length $w+6$; its area is $84$ square units?

Answer: $w(w+6)=84$. Sets the product of width and length (width plus 6) equal to the given area.

Flashcard 6: Which equation models: A gym charges $25 per month plus a $40 sign-up fee; total after $m$ months is $C$?

Answer: $C=25m+40$. Adds the monthly fees for m months to the one-time sign-up fee.

Flashcard 7: Which equation models: The perimeter $P$ of a rectangle with length $l$ and width $w$?

Answer: $P=2l+2w$. Computes the perimeter by adding twice the length and twice the width.

Flashcard 8: Which equation models: A taxi charges a $4 fee plus $2 per mile for $m$ miles, total cost $C$?

Answer: $C=4+2m$. Represents the total cost as the fixed fee plus the per-mile charge times the number of miles.

Flashcard 9: Which equation models: The sum of angles in a triangle is $180^\circ$; if angles are $x$, $x$, and $y$, what equation relates them?

Answer: $2x+y=180$. Sums twice one angle and the other angle to equal the total interior angles of a triangle.

Flashcard 10: Which equation models: You split $60 equally among $n$ friends; each friend gets $x$ dollars?

Answer: $x=\frac{60}{n}$. Divides the total money by the number of friends to find each person's share.

Flashcard 11: Which equation models: You have $50 and spend \x$; remaining money is$R$?

Answer: $R=50-x$. Calculates the remaining money by subtracting the amount spent from the initial $50.

Flashcard 12: Which equation models: The average of $a$, $b$, and $c$ is $M$?

Answer: $M=\frac{a+b+c}{3}$. Computes the arithmetic mean by summing the values and dividing by 3.

Flashcard 13: Which equation models: A jacket originally costs $p$ dollars and is discounted by $20\%$; sale price is $S$?

Answer: $S=0.8p$. Applies an 80% factor to the original price to account for the 20% discount.

Flashcard 14: Which equation models: The area $A$ of a triangle with base $b$ and height $h$?

Answer: $A=\frac{1}{2}bh$. Determines the area by multiplying the base and height, then dividing by 2.

Flashcard 15: Which equation models: The number $y$ is $5$ more than one-third of $x$?

Answer: $y=\frac{1}{3}x+5$. Adds 5 to one-third of x to obtain y.

Flashcard 16: Which equation models: The number $y$ is $12$ less than twice $x$?

Answer: $y=2x-12$. Expresses y as twice x reduced by 12.

Flashcard 17: Which equation models: A recipe uses $\frac{3}{4}$ cup of sugar per batch; for $b$ batches, total sugar is $S$ cups?

Answer: $S=\frac{3}{4}b$. Multiplies the sugar per batch by the number of batches to find total sugar needed.

Flashcard 18: Which equation models: A line has slope $3$ and $y$-intercept $-2$; what is its equation in slope-intercept form?

Answer: $y=3x-2$. Applies the slope-intercept form $y=mx+b$ with slope 3 and y-intercept -2.

Flashcard 19: Which equation models: The number of minutes $m$ is $60$ times the number of hours $h$?

Answer: $m=60h$. Converts hours to minutes by multiplying by 60.

Flashcard 20: Which equation models: The total cost $C$ for $n$ items at $8 each with a $5 coupon off the total?

Answer: $C=8n-5$. Subtracts the coupon value from the total cost of n items at $8 each.

Flashcard 21: Which equation models: Three times a number $n$ decreased by $5$ is $19$?

Answer: $3n-5=19$. Represents three times n minus 5 equaling 19.

Flashcard 22: Which equation models: The distance $d$ traveled at speed $r$ for time $t$?

Answer: $d=rt$. Expresses distance as the product of rate and time.

Flashcard 23: Which equation models: A number $x$ increased by $7$ equals $15$?

Answer: $x+7=15$. Models the situation where adding 7 to x results in 15.

Flashcard 24: Which equation models: You deposit $200 and then add $15 each week for $w$ weeks; total is $T$?

Answer: $T=200+15w$. Adds the weekly additions for w weeks to the initial deposit.