Question 52196: a childs bank contains 70 coins consisting of nickels and dimes that have a total value of $5.55. how many of each kind of coin are there?
Answer by blubunny01(20)   (Show Source):
You can put this solution on YOUR website! The problem asks you to look for two unknowns: # nickels, and # dimes.
Let x = # nickels.
Let y = # dimes.
We know that there are a total of 70 coins. So, to put this into equation form, we have: x + y = 70
We also know that the total value (sum) of the coins is $5.55. Again, to put this into equation form, we have: 0.05x + 0.10y = 5.55
(multiply each variable by the amount of money it's worth to find out the total sum for each type of coin, then add the totals together)
Now you have two equations for two unknowns, and there are several ways to solve these types of problems. For simplicity, I'll use the substitution method.
I will take x + y = 70 and solve for y:
y = 70 - x
Now, I will plug in this value into the second equation, and solve for x:
0.05x + 0.10(70 - x) = 5.55
0.05x + 7 - 0.10x = 5.55
-0.05x = -1.45
x = 29
Now, I can use this x value in the original equation to find y:
x + y = 70
29 + y = 70
y = 41
This means that there are 29 nickels and 41 dimes.
|
|
|
