In Vanessa's coin bank there are 4 times as many quarters as nickels, 2 fewer dimes than nickels, and 15 pennies. The total amount in the bank is $5.80. How many of each coin are in the bank?
A. Assign a variable to the unknown quantity.
B. Write an equation you can use to find the unknown quantity.
C. Solve and check the equation you wrote. Show your work.
nickels --- x
quarters -- 4x
dimes ----- x-2
5x + 25(4x) + 10(x-2) + 15 = 580
solve for x, then sub back into my definitions
Using that equation it comes up to $5.70 not $5.80..?
In that case your question is flawed.
since x must come out to a whole number ....
5x + 25(4x) + 10(x-2) + 15 = 580
5x + 100x + 10x - 20 + 15 = 580
115x = 585
x = 5.08...
so there is no solution.
Check your typing
Thanks. Typing is correct .. Question is flawed. Will let teacher know. Appreciate your help!
A. Let's assign variables to the unknown quantities:
Let's let x be the number of nickels.
Since there are 4 times as many quarters as nickels, the number of quarters is 4x.
And since there are 2 fewer dimes than nickels, the number of dimes is x - 2.
B. Now let's write an equation for the total value of the coins:
The value of the nickels is 5 cents each, so the value of x nickels is 5x cents.
The value of the quarters is 25 cents each, so the value of 4x quarters is 100x cents.
The value of the dimes is 10 cents each, so the value of (x - 2) dimes is 10(x - 2) cents.
And the value of the pennies is 1 cent each, so the value of 15 pennies is 15 cents.
The total value is $5.80, which is equivalent to 580 cents.
So the equation is: 5x + 100x + 10(x - 2) + 15 = 580
C. Now let's solve the equation and check the solution:
First, distribute the 10 to x and -2: 5x + 100x + 10x - 20 + 15 = 580
Combine like terms: 115x - 5 = 580
Add 5 to both sides: 115x = 585
Divide both sides by 115: x = 5
So there are 5 nickels, 4(5) = 20 quarters, and 5 - 2 = 3 dimes.
To check the solution, let's calculate the total value:
5(5) + 100(20) + 10(3) + 15 = 580 cents
25 + 2000 + 30 + 15 = 580 cents
2070 + 45 = 580 cents
580 cents = 580 cents.
Therefore, the solution is valid: there are 5 nickels, 20 quarters, 3 dimes, and 15 pennies in Vanessa's coin bank.