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

Answer:

103 dimes and 108 quarters

Step-by-step 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 $D = 211 - Q$

$D = 211 - 108$

$D = 103$