SOLUTION: Hi In march 2008 Benny increased his expenditure by 1/4 Joyce decreased hers by $20 an ah seng decreased his by 50%. They now spent the same amount of money. If they spent $590 in

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Question 1206744: Hi
In march 2008 Benny increased his expenditure by 1/4 Joyce decreased hers by $20 an ah seng decreased his by 50%. They now spent the same amount of money. If they spent $590 in February 2008 how much did Benny spend in march 2008.
Thanks





Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Let x be the amount Benny spent in February; then the amount he spent in March was (5/4)x.

Let y be the amount Joyce spent in February; then the amount she spent in March was y-20.

Let z be the amount Ahseng spent in February; then the amount he spent in March was (1/2)x.

The amounts they spent in March were all the same.

Knowing the amounts they spent in March were the same, express the amounts they spent in March in terms of a single variable. Arbitrarily, we can choose to represent all the amounts in terms of x.

Benny: (5/4)x

Joyce:
(5/4)x=y-20
y=(5/4)x+20

Ahseng:
(5/4)x=(1/2)z
z=(5/2)x

The total they spent in February was $590:

x%2By%2Bz=590
x%2B%28%285%2F4%29x%2B20%29%2B%28%285%2F2%29x%29=590
Multiply by 4 to clear fractions:

4x%2B5x%2B80%2B10x=2360
19x=2280
x=2280%2F190=120

ANSWER: The amount Benny spent in March was (5/4)x = $150.

CHECK:
Benny: February x=$120 March (5/4)x=$150
Joyce: February (5/4)x+20 = $170 March $170-$20=$150
Ahseng: February (5/2)x=$300 March (1/2)$300=$150

The March amounts are the same

The February total is $120+$170+$300 = $590