Question

Shelly has $5.55 in Nichols dimes and quarters in her piggy bank. There are 44 coins altogether with three more quarters and dimes. How many of each type of coin does she have?

a) 18 quarters, 29 dimes
b) 21 quarters, 23 dimes
c) 26 quarters, 18 dimes
d) 29 quarters, 15 dimes

Answer 1

Shelly has 8 quarters and 36 dimes in her piggy bank.

Step-by-step explanation:

Let's solve this problem using a system of equations. Let x represent the number of quarters and y represent the number of dimes. We can set up two equations based on the information given:

• x + y = 44 (There are 44 coins in total)
• 0.25x + 0.10y = 5.55 (The value of the coins adds up to $5.55)

We can solve this system of equations using substitution or elimination. Let's use substitution for this example:

1. Rewrite the first equation as x = 44 - y.
2. Substitute x in the second equation: 0.25(44 - y) + 0.10y = 5.55.
3. Simplify and solve for y: 11 - 0.25y + 0.10y = 5.55. Combine like terms: -0.15y = -5.45. Divide both sides by -0.15 to solve for y: y = 36.33.
4. Since we can't have a fraction of a coin, the closest whole number for y is 36. Now substitute this value back into the first equation to find x: x + 36 = 44. Subtract 36 from both sides: x = 8.

Therefore, Shelly has 8 quarters and 36 dimes.