jacksonmjl91
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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?

Respuesta :

mhanifa

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
xKelvin

Answer:

[tex]135+\frac{1}{2}x=143-\frac{1}{4}x[/tex]

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:

[tex]D=135+\frac{1}{2}x[/tex]

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:

[tex]M=143-\frac{1}{4}x[/tex]

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

[tex]D=M[/tex]

Substitute them for their respective equations to acquire:

[tex]135+\frac{1}{2}x=143-\frac{1}{4}x[/tex]

Notes:

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

[tex]540+2x=572-x[/tex]

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

[tex]3x=32[/tex]

Divide both sides by 3:

[tex]x=32/3\approx10.67[/tex]

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

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