A family has a coin jar that is now full. The children count the change and calculate the total value to be $29.42. Let Q represent the number of quarters and use the information below to find the number of each coin.
There are:
138 more dimes than quarters
2 times as many nickels as quarters
28 more than 14 times as many pennies as quarters
In the jar there was:
Quarters,
dimes,
nickels, and
pennie
looks like everything is referenced in terms of quarters, so start with :
let the number of quarters be x
dimes ---- x+138
nickels ---- 2x
pennies ---- 14x + 28
Now that you have the NUMBER of coins defined, we go for the VALUE of those coins
25x + 10(x+138) + 5(2x) + 1(14x+28) = 2942
I am sure you can finish that
wow thank you so much!!
To find the number of each type of coin, let's break down the given information:
1. "138 more dimes than quarters": Let's assume the number of quarters is Q, so the number of dimes would be Q + 138.
2. "2 times as many nickels as quarters": Let's assume the number of quarters is Q, so the number of nickels would be 2Q.
3. "28 more than 14 times as many pennies as quarters": Let's assume the number of quarters is Q, so the number of pennies would be 14Q + 28.
Now that we have expressions for each type of coin in terms of the number of quarters, we can set up an equation to find the number of quarters:
Value of Quarters (in cents): 25Q
Value of Dimes (in cents): 10(Q + 138) = 10Q + 1380
Value of Nickels (in cents): 5(2Q) = 10Q
Value of Pennies (in cents): 1(14Q + 28) = 14Q + 28
Now, let's add all the values together and equate it to the total value of $29.42, which is 2942 cents:
25Q + 10Q + 1380 + 10Q + 14Q + 28 = 2942
Combining like terms:
59Q + 1408 = 2942
Subtracting 1408 from both sides:
59Q = 1534
Dividing both sides by 59:
Q = 26
So, there are 26 quarters in the jar.
Now, let's find the number of each type of coin:
Number of Dimes = Q + 138 = 26 + 138 = 164
Number of Nickels = 2Q = 2 * 26 = 52
Number of Pennies = 14Q + 28 = 14 * 26 + 28 = 392 + 28 = 420
Therefore, in the jar, there are:
- 26 quarters
- 164 dimes
- 52 nickels
- 420 pennies