Question

isabella collected a bunch of dimes and quarters for her school fundraiser she collected a total of 211 coins and a total of 37.30 how many dimes and how many quarters did she collect

Answer 1

103 dimes and 108 quarters

Explanation:

Given

`Value = \$37.30`

`Amount = 211`

Required

Determine the number of each coin collected

Represent dimes with D and quarters with Q.

`1\ D= \$0.10`

`1\ Q= \$0.25`

So:

`0.10D + 0.25Q = 37.30` --- Value

`D + Q = 211` --- Amount

Make D the subject in
`D + Q = 211`

`D = 211 - Q`

Substitute 211 - Q for D in
`0.10D + 0.25Q = 37.30`

`0.10(211 - Q) + 0.25Q = 37.30`

Open brackets

`21.1 - 0.10Q + 0.25Q = 37.30`

Collect Like Terms

`- 0.10Q + 0.25Q = 37.30 - 21.1`

`0.15Q = 16.2`

Make Q the subject

`Q = 16.2/0.15`

`Q = 108`

Substitute 108 for Q in
`D = 211 - Q`

`D = 211 - 108`

`D = 103`