The equation 3x + 4y = 36 represents the relationship between the number of small boxes, x… — SAT

The equation $3x + 4y = 36$ represents the relationship between the number of small boxes, $x$ , and large boxes, $y$ , that can fit in a delivery van. If the van is loaded with exactly 6 large boxes, what is the number of small boxes that can also fit in the van?

Answer: 4

Answer

The number of small boxes that can also fit in the van is 4.

Substituting

y = 6

into the equation

3x + 4y = 36

gives

3x + 24 = 36

. Subtracting 24 from both sides results in

3x = 12

. Dividing both sides by 3 yields

x = 4

. Thus, the number of small boxes that can fit is 4.

Step-by-Step Solution

Substitute 6 for

y

in the equation

3x + 4y = 36

3x + 4(6) = 36

The variable

y

represents the number of large boxes, which is given as 6.

Simplify the multiplication in the equation.

3x + 24 = 36

To simplify the terms before solving for

x

Subtract 24 from both sides of the equation.

3x = 12

To isolate the variable term

3x

on one side of the equation.

Divide both sides of the equation by 3.

x = 4

To solve for

x

, the number of small boxes.

Key Concept

Evaluating and solving a linear equation in two variables given the value of one variable.

Estimated Time:45s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic