MATH SOLVE

2 months ago

Q:
# Jenny has saved $3,800 over the last 12 months. She saved either $250 or $350 a month. During the 12 month period, how many times did Jenny save $250 for the month?

Accepted Solution

A:

Answer:Jenny save 4 times [tex]\$ 250[/tex] for the monthStep-by-step explanation:Given Jenny has saved [tex]\$3,800[/tex] over the last 12 months. She saved either [tex]\$250[/tex] or [tex]\$350[/tex] a month.Let the number of months to save [tex]\$250[/tex] be xLet the number of months to save [tex]\$350[/tex] be yTotal period is 12 month.[tex]x+y=12 \ \ \ \ equation\ 1[/tex]Jenny has saved $3,800 over the last 12 months.[tex]250x+350y=3800[/tex]Dividing both side from 50 we get,[tex]\frac{250}{50}x+\frac{350}{50}y= \frac{3800}{50}[/tex][tex]5x+7y=76 \ \ \ \ equation\ 2[/tex]Now Multiplying equation 1 by 5 we get,[tex]5\times(x+y)=5\times 12\\5x+5y=60\ \ \ \ equation \ 3[/tex]Now Subtracting Equation 3 by equation 2 we get,[tex](5x+7y=76)-(5x+5y=60)\\2y=16\\y=\frac{16}{2}= 8[/tex]Substituting the value of y in equation 1 we get,[tex]x+y=12\\x+8=12\\x=12-8\\x=4[/tex]∴ Jenny save 4 Months of [tex]\$ 250[/tex] and 8 Months of [tex]\$ 350[/tex]in a 12 month duration