Question

A baker is building a rectangular solid box from cardboard to be able to safely deliver a birthday cake. The baker wants the volume of the delivery box to be 360 cubic inches. If the width of the delivery box is 3 inches longer than the length and the height is 4 inches longer than the length, what must the length of the delivery box be?
2 inches
5 inches
8 inches
9 inches

Answer 1

Answer:

5

Step-by-step explanation:

Answer 2

Solution is 8 in

Let´s call dimensions of the box

• x  the length of the box

• y the width  of the box    and

• h the height  of the box

According to the problem statement

y = x + 3     and    h = 4 in

The volume of the box is:

V = x×y×h       V = 360 in³

Then  V = x × ( x + 3 ) × 4     ( by substitution of y as a function of x )

360 = x × ( x + 3 ) × 4

Simplifying by 4

90 =  x × ( x + 3 )

90 = x² + 3x

We got a second degree equation, solving for x

x² + 3×x - 90 = 0

x₁,₂ = ( -3 ± √ (3)² + 4×90 )/2   ⇒   x₁,₂ = ( - 3 ± 19,21 )/2

x₁   ⇒  is a negative value    x = - 11,1  so we dismiss such solution

x₂  = 16.21/2

x₂  =  8.1 in

rounding to the nearest integer number we get the value for the length f the box

x₂ = 8 in        ⇒ x = 8 in

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