Question

i have 30 coins. some of them are dimes, and some of them are quarters. in total, i have $4.05. how many of each coin do i have?

Answer 1

Answer: 23 dimes & 7 quarters

Step-by-step explanation:

• Dimes = 10¢ = $0.10
• Quarters = 25¢ = $0.25
• Number of dimes = x
• Number of quarters = y

You can create two equations:

$\left \{ {{x + y = 30} \atop {0.10x + 0.25y =4.05}} \right.$

Rearrange x + y = 30:

$y=30-x$

Substitute it into the x-value of the other equation & solve:

$0.10x + 0.25y =0.10x + 0.25(30-x)=4.05\\0.10x+7.5-0.25x=4.05\\0.10x-0.25x=4.05-7.5\\-0.15x=-3.45\\x=\frac{-3.45}{-0.15} =23$

With the x-value, substitute it back to the original equation to find y-value:

$y=30-x=30-23=7$

Therefore, there are 23 dimes & 7 quarters.

Answer 2

Answer:

23 dimes and 7 quarters

Step-by-step explanation:

The least amount of money using the most coins are 30 dimes ($3.00)