Question 1206744
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Let x be the amount Benny spent in February; then the amount he spent in March was (5/4)x.<br>
Let y be the amount Joyce spent in February; then the amount she spent in March was y-20.<br>
Let z be the amount Ahseng spent in February; then the amount he spent in March was (1/2)x.<br>
The amounts they spent in March were all the same.<br>
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.<br>
Benny: (5/4)x<br>
Joyce:
(5/4)x=y-20
y=(5/4)x+20<br>
Ahseng:
(5/4)x=(1/2)z
z=(5/2)x<br>
The total they spent in February was $590:<br>
{{{x+y+z=590}}}
{{{x+((5/4)x+20)+((5/2)x)=590}}}
Multiply by 4 to clear fractions:<br>
{{{4x+5x+80+10x=2360}}}
{{{19x=2280}}}
{{{x=2280/190=120}}}<br>
ANSWER: The amount Benny spent in March was (5/4)x = $150.<br>
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<br>
The March amounts are the same<br>
The February total is $120+$170+$300 = $590<br>