Answer:
Number of pennies: 125
Number of nickels: 95
Number of dimes: 95
Explanation:
Let's call x the number of pennies, y the number of nickels, and z the number of dimes.
If the child has 315 coins, we get:
x + y + z = 315
Additionally, they worth $15.50, so
0.01x + 0.05y + 0.10z = 15.50
Because a penny has a value of $0.01, a nickel has a value of $0.05 and a dime has a value of $0.10
Finally, the bag contains the same number of nickels and dimes, so
z = y
Therefore, we have the following system of equation:
x + y + z = 315
0.01x + 0.05y + 0.10z = 15.50
z = y
Replacing the last equation on the first one, we get:
x + y + z = 315
x + y + y = 315
x + 2y = 315
Then, we can solve the equation for x, so
x + 2y - 2y = 315 - 2y
x = 315 - 2y
Now, we need to replace z = y and x = 315 - 2y on the second equation of the system
0.01x + 0.05y + 0.10z = 15.50
0.01(315 - 2y) + 0.05y + 0.10y = 15.50
0.01(315) - 0.01(2y) + 0.05y + 0.10y = 15.50
3.15 - 0.02y + 0.05y + 0.10y = 15.50
3.15 + 0.13y = 15.50
And solve for y
3.15 + 0.13y - 3.15 = 15.50 - 3.15
0.13y = 12.35
0.13y/0.13 = 12.35/0.13
y = 95
With the value of y, we can find the value of x and z as follows
x = 315 - 2y
x = 315 - 2(95)
x = 315 - 190
x = 125
z = y
z = 95
Then, there are 125 pennies, 95 nickels, and 95 dimes
Therefore, the answers are
Number of pennies: 125
Number of nickels: 95
Number of dimes: 95