Question

The length and a quarter of the width of a rectangle add up to 7 in, while the length and the width add up to 10 in. What are the rectangle’s length and width?

Answer 1

The length is 6, and the width is 4.

Explanation:

The length and width add up to 10. 6 + 4 = 10.

A quarter of the width plus the length = 7. A quarter of 4 = 1. 1 + 6 = 7

Answer 2

Width is 4 inches, Length is 6 inches

Explanation:

Let us set a variables, l for length, and w for width. Now, we can write two expressions with the given information:

1. The length, l, and one quarter of the width, w, add up to 7in. Therefore,:

l+0.25w=7

2. The length, l, and the width, w, add up to 10in. Therefore,:

l+w=10

Let us now subtract the first equation from the second to find the variable, w. When we do this, we should make sure that we are subtracting on both sides:

`l+w-(l+0.25w)=10-7\\l+w-l-0.25w=3\\0.75w=3\\w= 4`

Now, let us substitute this 4 into w of the equation to obtain l:

l+w=10

l+4=10

l=6

Therefore, the width of the rectangle is 4 inches and the length of the rectangle is 6 inches.

I hope this helps! Please let me know if you have any further questions :)