Three siblings have decided to pool their money to buy their parents a gift for their anniversary. They need to save $224.50 in total. Each sibling has a different rate of pay and works a different number of hours. Nancy earns $10.70 per hour. • Marc earns $11.30 per hour and always works 5 more hours per week than Nancy. • Kara babysits and earns $9 per hour and always works 2 hours less per week than Nancy. How many hours in a week must each sibling work in order to reach their goal of $224.50?

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ajinems ajinems · Answer 1 · 2022-03-10T17:29:42+01:00

The number of hours each sibling must work each week to reach their goal of $224.50 is as follows:

The total amount of money that needs to be saved = $224.50

Total amount of money Nancy earn = $10.70 per hour.

Total amount of money Marc earn = $11.30 per hour

Total amount of money Kara earn = $9 per hour

Number of hours Nancy works = X hours

Number of hours Marc works = 5 + X hours

Number of hours Kara works = X - 2 hours

To calculate the amount each earn according to the number of hours they worked the following is carried out;

10.70(X) + 11.30( 5+X) + 9(x-2) = 224.50

10.70x + 56.5 + 11.30x + 9x - 18 = 224.50

Collect the like terms together

10.70x+11.30x+9x +56.5-18 = 224.50

31x + 38.5 =224.50

31x =224.50 - 38.5

31x = 186

X = 186/31

X = 6

Therefore Nancy works for 6 hours

Marc works for 5 + X = 5+6 = 11 hours

Kara works for x- 2= 6-2 = 4 hours

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