Question

Francie has $5.00 in dimes and quarters. The number of dimes is 1 more than the number of quarters. How many of each coin does she have?

a) 10 dimes and 9 quarters.
b) 7 dimes and 8 quarters.
c) 3 dimes and 4 quarters.
d) 8 dimes and 7 quarters.

Answer 1

Using a system of equations, we find that Francie has 14 quarters and 15 dimes given that she has a total of $5.00 in dimes and quarters, with the dimes being 1 more than the number of quarters. None of the provided options match this solution.

Step-by-step explanation:

The question is asking us to determine how many dimes and quarters Francie has if she has $5.00 in total, with the number of dimes being 1 more than the number of quarters. We can solve this problem using a system of equations. Let's define Q as the number of quarters and D as the number of dimes. The value of a dime is 10 cents, and the value of a quarter is 25 cents. Since 1 dollar equals 100 pennies, we have two equations:

• 10D + 25Q = 500 (because Francie has $5.00, which is 500 cents)
• D = Q + 1 (because there is one more dime than quarters)

Now we substitute the second equation into the first to find the number of quarters:

• 10(Q + 1) + 25Q = 500
• 10Q + 10 + 25Q = 500
• 35Q + 10 = 500
• 35Q = 490
• Q = 14

Now that we know Q is 14, we can find D by plugging Q back into the second equation:

• D = Q + 1
• D = 14 + 1
• D = 15

Therefore, Francie has 14 quarters and 15 dimes. This means none of the provided options (a, b, c, or d) are correct.