7. Your piggy bank contains quarters and dimes. Ihere are 572 coins in the piggy bank totaling $$ \$ 92 $$. How many quarters and dimes are in the piggy bank?

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UpStudy AI · Accepted Answer

To determine the number of quarters and dimes in the piggy bank, let's set up a system of equations based on the information provided.

### Let:
- $$ q $$ = number of quarters
- $$ d $$ = number of dimes

### Given:
1. **Total number of coins:**
   $$
   q + d = 572
   $$
2. **Total value of the coins:**
   $$
   0.25q + 0.10d = 92
   $$
   *(Note: Converted dollars to cents to avoid decimals: $$ 25q + 10d = 9200 $$ cents)*

### Solving the System of Equations:

1. **Express one variable in terms of the other using the first equation:**
   $$
   d = 572 - q
   $$

2. **Substitute $$ d $$ into the second equation:**
   $$
   25q + 10(572 - q) = 9200
   $$
   
3. **Distribute and simplify:**
   $$
   25q + 5720 - 10q = 9200
   $$
   $$
   15q + 5720 = 9200
   $$
   
4. **Isolate $$ q $$:**
   $$
   15q = 9200 - 5720
   $$
   $$
   15q = 3480
   $$
   $$
   q = \frac{3480}{15}
   $$
   $$
   q = 232
   $$
   
5. **Find $$ d $$ using the first equation:**
   $$
   d = 572 - 232 = 340
   $$

### **Conclusion:**
- **Number of Quarters:** 232
- **Number of Dimes:** 340

### **Verification:**
- **Value from Quarters:** $$ 232 \times \$0.25 = \$58.00 $$
- **Value from Dimes:** $$ 340 \times \$0.10 = \$34.00 $$
- **Total Value:** $$ \$58.00 + \$34.00 = \$92.00 $$ *(Which matches the given total)*

Therefore, the piggy bank contains **232 quarters** and **340 dimes**.
There are 232 quarters and 340 dimes in the piggy bank.

Your piggy bank contains quarters and dimes. Ihere are 572 coins in the piggy bank totaling . How
many quarters and dimes are in the piggy bank?

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Your piggy bank contains quarters and dimes. Ihere are 572 coins in the piggy bank totaling . How many quarters and dimes are in the piggy bank?