A bag contains 37 coins, some dimes and some quarters. The total amount of
money in the bag is . How many dimes and how many quarters are in the
bag?
dimes

Question

A bag contains 37 coins, some dimes and some quarters. The total amount of money in the bag is $$ \$ 5.05 $$. How many dimes and how many quarters are in the bag? dimes

UpStudy AI · Accepted Answer

Let's denote the number of dimes by $$ d $$ and the number of quarters by $$ q $$.

We have two pieces of information:

1. The total number of coins is 37:
$$
d + q = 37
$$

2. The total value of the coins is \$5.05. Since a dime is worth 10 cents and a quarter is worth 25 cents, we have:
$$
10d + 25q = 505
$$
(Note: \$5.05 is equal to 505 cents.)

Now, solve the system of equations step by step.

**Step 1: Express one variable in terms of the other.**

From the first equation:
$$
d = 37 - q
$$

**Step 2: Substitute into the second equation.**
$$
10(37 - q) + 25q = 505
$$

**Step 3: Simplify and solve for $$ q $$.**
$$
370 - 10q + 25q = 505
$$
$$
370 + 15q = 505
$$
$$
15q = 505 - 370
$$
$$
15q = 135
$$
$$
q = \frac{135}{15} = 9
$$

**Step 4: Find the number of dimes.**
$$
d = 37 - q = 37 - 9 = 28
$$

Thus, there are $$ 28 $$ dimes and $$ 9 $$ quarters in the bag.
There are 28 dimes and 9 quarters in the bag.

A bag contains 37 coins, some dimes and some quarters. The total amount of
money in the bag is . How many dimes and how many quarters are in the
bag?
dimes

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A bag contains 37 coins, some dimes and some quarters. The total amount of money in the bag is . How many dimes and how many quarters are in the bag? dimes

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A bag contains 37 coins, some dimes and some quarters. The total amount of
money in the bag is . How many dimes and how many quarters are in the
bag?
dimes