Question

A coin purse contains d dimes and q quarters. There are 35 coins in the purse, and the total value of the coins is $5.60. Create the system of linear equations and use it to find how many dimes and quarters are in the purse.

Answer 1

Answer:

14 dimes, 21 quarters

Step-by-step explanation:

Represent dimes with d and quarters with q.

So: 35 coins means

$d + q = 35$

1 dime = $0.10 and 1 quarter = $0.25. So, a value of $5.60 means

$0.10d + 0.25q = 5.60$

So, the system of equations is:

$d + q = 35$

$0.10d + 0.25q = 5.60$

Make d the subject in $d + q = 35$

$d = 35 - q$

Substitute 35 - q for d in $0.10d + 0.25q = 5.60$

$0.10d + 0.25(35 - q) = 5.60$

Open bracket

$0.10d + 8.75 - 0.25q = 5.60$

Collect Like Terms

$0.10d - 0.25q = 5.60 - 8.75$

$-0.15q = -3.15$

Solve for q

$q = \frac{-3.15}{-0.15}$

$q = 21$

Substitute 21 for q in $d = 35 - q$

$d = 35 - 21$

$d = 14$