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

Answer:

• 10.66 weeks

Step-by-step 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

Answer 2

Answer:

$135+\frac{1}{2}x=143-\frac{1}{4}x$

Step-by-step 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:

$D=135+\frac{1}{2}x$

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:

$M=143-\frac{1}{4}x$

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

$D=M$

Substitute them for their respective equations to acquire:

$135+\frac{1}{2}x=143-\frac{1}{4}x$

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.