Question

Erin weighs 135 pounds and is gaining ½ pound each week. Miranda weighs 143 pounds and is losing ¼ pound each week. Write an equation that could be used to determine x, the number of weeks that it will take until the two girls weigh the same amount?

Answer 1

`135+(1)/(2)x=143-(1)/(4)x`

Explanation:

Let E represent Erin’s weight, and let M reprevent Miranda’s weight.

And let x represent the amount of week that passes.

Eric is currently 135 pounds. However, she is gaining 1/2 pounds per week x.

Hence, we can write the following equation:

`D=135+(1)/(2)x`

Miranda currently weights 143 pounts. However, she is losing 1/4 pounds per week x.

Since she is losing weight, 1/4 is negative. Hence:

`M=143-(1)/(4)x`

When the two girls weigh the same, D=M. Thus:

`D=M`

Substitute them for their respective equations to acquire:

`135+(1)/(2)x=143-(1)/(4)x`

Notes:

To solve, first eliminate the fractions by multiplying everything by 4. This yields:

`540+2x=572-x`

Add x to both sides. Subtract 540 from both sides:

`3x=32`

Divide both sides by 3:

`x=32/3\approx10.67`

Hence, it will take about 11 weeks for the girls to weigh the same.

Answer 2

• 10.66 weeks

Explanation:

Number of weeks is x

• 135 + 1/2x = 143 - 1/4x
• 1/2x + 1/4x = 143 - 135
• 3/4x = 8
• x = 32/3 = 10.66 weeks