Question

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?

Answer 1

4 times

Explanation:

Let,

250 = x

350 = y

x + y = 12

250x + 350y = 3,800

Solve the system.

x = 4 and y = 8

Therefore, Jenny saved $250 for 4 months and $350 for 8 months.

Answer 2

Jenny save 4 times
`\$ 250` for the month

Explanation:

Given Jenny has saved
`\$3,800` over the last 12 months.

She saved either
`\$250` or
`\$350` a month.

Let the number of months to save
`\$250` be x

Let the number of months to save
`\$350` be y

Total period is 12 month.

`x+y=12 \ \ \ \ equation\ 1`

Jenny has saved $3,800 over the last 12 months.

`250x+350y=3800`

Dividing both side from 50 we get,

`(250)/(50)x+(350)/(50)y= (3800)/(50)`

`5x+7y=76 \ \ \ \ equation\ 2`

Now Multiplying equation 1 by 5 we get,

`5*(x+y)=5* 12\\5x+5y=60\ \ \ \ equation \ 3`

Now Subtracting Equation 3 by equation 2 we get,

`(5x+7y=76)-(5x+5y=60)\\2y=16\\y=(16)/(2)= 8`

Substituting the value of y in equation 1 we get,

`x+y=12\\x+8=12\\x=12-8\\x=4`

∴ Jenny save 4 Months of
`\$ 250` and 8 Months of
`\$ 350`in a 12 month duration