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Question

I need a help to solve this problem.

Julie’s weekly allowance is $11.80 more than Steven’s.  Steven spends $12.50 more than Julie every week.  Julie spends 5/11 of her allowance every week.  Steven saves 1/2 as much as Julie every week.  How much did Steven spend after 7 weeks?

 

Thanks in advance..

Answer

Allowance

Julie -> 11u

Steven -> 11u – 11.80

 

Spending

Julie -> 5u

Steven -> 5u + 12.50

 

Savings

Julie -> 11u – 5u = 6u

Steven -> 3u   (half as much as Julie)

 

Allowance = Spending + Savings

11u – 11.80 = 5u + 12.50 + 3u

3u = 24.30

1u = 8.10

 

In one week, Steven spent 5(8.10) + 12.50 = 53

Therefore, in 7 weeks, he spent 53 x 7 = $371.00

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Key to solve: Be bold to move along the question and write down all details bit by bit…. and compare along the way. Good luck to all!

                                          Julie                Steven    

Weekly allowance          u+11.80           u              (J’s weekly allowance is $11.80>S’s)

Spends                             s                       s+12.50   (S spends $12.50 > J every week)


Spends                             5p                                     (J spends 5/11 of her allowance)

Saves                                6p                      3p          (Bal of 11p),(S saves 1/2 as much as J weekly)


Spends                              5p                  5p +12.50 (deduce by comparing red lines)

Saves                                 6p                     3p

Add=allowance              11p                  8p+12.50    (then compare to 1st line at top)

11p – 8p-12.50 = 11.80

p= 8.10

5p+12.50 = 53 (Steven spends per week)

53 x 7 = $371# (Steven spends in 7 weeks)


Checking:

Spends                         5 (8.10)              5(8.10)+12.50 

Saves                            6 (8.10)                   3(8.10)

Add=Allowance         89.10                      77.30       (Diff = 11.80)  –> OK!

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