Christopher and Sophia bought a store to start a new cake shop. The store has an area of 75 square meters. The length of the store is 10 meters more than its width. What is the length of the store?

Given:

Area of store = 75 m^2

Length = 10 meters more than its width

Formula for the area of a rectangle:

A = lw

Solution:

The given statement for length can be represented as,

l = 10 + w

A = (10 + w)(w)

Susbstitute the given value of A to the formula.

75 = (10 + w)(w)

75 = w^2 + 10w

transpose 75 on the other side of the equation, note that when transposing a number the sign changes.

= w^2 + 10w - 75

Now we need to find the value of w by factoring the equation. In factoring a quadratic equation, we must look for two numbers that when added, the sum is the 2nd value of the quadratic equation, and when multiplied the product is the 3rd value of the quadratic equation. The numbers, -5 and 10 satisfies the condition.

( w - 5)(w + 10)

Since we are given two values, we must look for the positive value of w because we cannot have a negative width. We can find the value by equating the factors to 0

w - 5 = 0

w = 5

w  + 10 = 0

w = -10

Width = 5 meters

Now we know that the width is 5, we need to solve for length,

l = 10 + w

l = 10 + 5

l = 15

Check:

A = (5m)(15m)

A = 75m^2

Final answer:

Length = 15 meters