Answer
We have 8 nickels.
We have 25 dimes.
We have 50 quarters.
Work Step by Step
Let X represent the number of nickels.
The number of dimes is 1 more than three times the number of nickels.
Three times the number of nickels means 3X
1 more than three times the number of nickels means 3X + 1.
So, the number of dimes is 3X + 1.
The number of quarters is twice the number of dimes. Since the number of dimes is 3X + 1, the number of quarters is (3X + 1) $\times$ 2 = 6X + 2.
One nickel is worth 5 cents, so we have X $\times$ 5 = 5X cents.
One dime is worth 10 cents, so we have (3X + 1) $\times$ 10 = 30X + 10 cents.
One quarter is worth 25 cents, so we have (6X + 2) $\times$ 25 = 150X + 50 cents.
In total, we have 15.40 dollars, which is equal to 1540 cents.
Thus, we set up the following equation:
5X + 30X + 10 + 150X + 50 = 1540
185X = 1480
Divide both sides by 185:
X = 8
We have 8 nickels.
We have 3X + 1 dimes, so we have 3 $\times$ 8 + 1 = 25 dimes.
We have 6X + 2 quarters, so we have 6 $\times$ 8 + 2 = 50 quarters.
