Test: Linear Equation Word Problems - SAT MCQ

If xy = 36 and x and y are integers, then x and y are both factors of 36. In order to minimize the value of x - y, we must find the greatest separation between x and y. The greatest separation between a factor pair is 1 - 36 = -35.

We should regard this as a “conversion” prob- lem from m days into a corresponding number of dollars.

The simplest approach is perhaps to choose simple values for x and y, like 2 and 3, and see which operator yields a true equation. Since (2 ÷ 3) × (3 ÷ 2) = 1, the answer is D.

The revenue is equal to the number of items sold times the price per item. If the restaurant typically sells n sandwiches per day, but today sold 50% more, it sold 1.5n sandwiches. If the price p was reduced 30%, today’s price is 0.70p. Therefore, the total revenue is (1.5n)(0.70p) = 1.05np.

Let x = the number of dollars David had to start.
If Carlos started with twice as much money as David, then Carlos started with 2x dollars. After Carlos gave David $12, Carlos had 2x - 12 dollars and David had x + 12 dollars. If Carlos still had $10 more than David, then
2x - 12 = 10 + x + 12
Simplify: 2x - 12 = x + 22
Add 12: 2x = x + 34
Subtract x: x = 34
Therefore, David started with $34 and Carlos started with 2($34) = $68, so they had $34 + $68 = $102 combined to start.

We calculate the price increase as 5% ⋅ $2.40. We have
5% ⋅ 2.40 = 0.05 ⋅ 2.40 = 0.1200 = 0.12
We must add the price increase to the old price.
2.40 + 0.12 = 2.52
The new price is, therefore, $2.52

We denote the number of hours by x. Then the total price is calculated as the price per hour ($12) times the number of workers times the number of hours (3). We obtain the equation
12 ⋅ 3 ⋅ x = 180
Simplifying this yields
36x = 180
Dividing by 36 gives
x = 180/36 = 5
Therefore, the three workers needed 5 hours for the job.

x + 4x = 300
Combining the like terms on the left, we get
5x = 300
Dividing by 5, we obtain that
x = 300/5 = 60
Therefore, the shorter piece has a length of 60 feet, while the longer piece has four times this length, that is 4 × 60 feet = 240 feet.

We denote the weight of a block by x. If 4 blocks weigh 28, then a block weighs x = 28/4 = 7

How many blocks weigh 70? Well, we only need to find 70/7 = 10. So, the answer is 10.

We know that C = 2πr where C is the circumference and r is the radius. So in this case
4 = 2πr

Dividing both sides by 2π gives
r = 4/2π = 2/π in ≈ 0.63in