Equations / Inequalities

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ACT Math › Equations / Inequalities

Questions 1 - 10

Give the lines y = 0.5x+3 and y=3x-2. What is the y value of the point of intersection?

Explanation

In order to solve for the x value you set both equations equal to each other (0.5x+3=3x-2). This gives you the x value for the point of intersection at x=2. Plugging x=2 into either equation gives you y=4.

If y=0.35(300 – 2y), what is the value of y to the nearest tenth?

61.8

51.2

65.0

62.3

Explanation

Distributing the 0.35 to both the 300 and **–**2y leaves y=105 – 0.7y

Adding 0.7y to both sides and dividing by 1.7 gives 61.8.

A car averages miles per gallon. If gas costs $\$ 3.04$ per gallon, which of the following is closest to how much the gas would cost for this car to travel $1\textup{,}642$ typical miles?

$\$156$

$\$50$

$\$51$

$\$155$

$\$17$

Explanation

To solve this problem you should divide the total number of miles $\left ( 1\textup{,}642\right )$ by the miles per gallon $\left ( 32\right )$ , and then multiply by the cost of gas per gallon $\left ( \$3.04\right)$ . This gives you $\$155.99$ , which is closest to $\$156$ .

The Teddy Bear Parade makes teddy bears. Their monthly fixed costs are $550. It costs $25 to make each bear and they sell for $50 each.

To make a profit of $750, how many teddy bears must be sold?

Explanation

Let = number of teddy bears sold.

Revenue:

Costs:

Profits = or

So the equation to solve becomes

So to make a profit of $750, 52 teddy bears must be sold.

Translate into an algebraic expression:

One third of the difference of a number and 3 equals five times the number.

$\frac{1}{3}\left ( x-3 \right )=5x$

$\frac{1}{3}x-3=5$

$\frac{1}{3}x-3=5x$

$\frac{1}{3}\left ( x+3 \right )= 5x$

$3\left ( x-3 \right )=5x$

Explanation

You have to form the difference first and must be enclosed in parentheses which gets multiplied by 1/3. The word "equals" means the "=" symbol

Three consecutive even numbers add to 42. What is the middle number?

$14$

$10$

$12$

$16$

$18$

Explanation

Let $x$ = 1st even number, $x+2$ = 2nd even number, and $x+4$ = 3rd even number.

Then the equation to solve becomes $x+(x+2)+(x+4)=42$ .

$3x+6=42$

Thus $x=12,x+2=14,\ and\ x+4=16$ , so the middle number is 14.

If 5 + x is 5 more than 5,what is the value of 2_x_?

Explanation

5 more than 5 = 10

5 + x = 10

Subtract 5 from each side of the equation: x = 5 → 2_x_ = 10

Three consecutive positive numbers have the sum of 15. What is the product of these numbers?

120

Explanation

Define the variables as x = the first number, x + 1, the second number, and x + 2 the thrid number.

The sum becomes x + x + 1 + x + 2 = 15 so 3x + 3 = 15. Subtract 3 from both sides of the equation to get 3x = 12 → 3x/3 = 12/3 → x = 4

The three numbers are 4, 5, and 6 and their product is 120.

Pets Plus makes bird houses. Their monthly fixed expenses are $750. The cost for each bird house is $15. The bird houses sell for $40.

If Pets Plus sells 50 bird houses, what is the profit?

$\$500$

$\$250$

$\$750$

$\$300$

$\$625$

Explanation

Let $x$ = the number of birdhouses sold each month.

$Revenue=40x$

$Costs=15x+750$

$Profit = Revenue-Costs$

$=40x-15x-750$

$=25x-750$

Substituting in 50 for $x$ gives an answer of 500, so the profit on 50 birdhouses is $500.

Three consecutive even numbers add to 42. What is the middle number?

$14$

$10$

$12$

$16$

$18$

Explanation

Let $x$ = 1st even number, $x+2$ = 2nd even number, and $x+4$ = 3rd even number.

Then the equation to solve becomes $x+(x+2)+(x+4)=42$ .

$3x+6=42$

Thus $x=12,x+2=14,\ and\ x+4=16$ , so the middle number is 14.

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