8. Ann and Betty together have $$ \$ 60 $$. Ann has $$ \$ 9 $$ more than twice Betty's amount. does each have? $$ 9 a+2 B=60 $$

Question

UpStudy AI · Accepted Answer

Let's solve the problem step by step.

**Problem Statement:**
- **Total Amount:** Ann and Betty together have \$60.
- **Relationship:** Ann has \$9 more than twice Betty's amount.

Let's define:
- Let $$ A $$ be the amount of money Ann has.
- Let $$ B $$ be the amount of money Betty has.

**Step 1: Translate the Problem into Equations**

Based on the problem statement, we can form the following equations:

1. **Total Amount Equation:**  
   $$ A + B = 60 $$

2. **Relationship Equation:**  
   Ann has \$9 more than twice Betty's amount:  
   $$ A = 2B + 9 $$

**Step 2: Substitute and Solve**

We can substitute the expression for $$ A $$ from the second equation into the first equation.

1. Substitute $$ A = 2B + 9 $$ into $$ A + B = 60 $$:
   $$ (2B + 9) + B = 60 $$

2. Combine like terms:
   $$ 3B + 9 = 60 $$

3. Subtract 9 from both sides:
   $$ 3B = 51 $$

4. Divide both sides by 3:
   $$ B = 17 $$

**Step 3: Find Ann's Amount**

Now that we know $$ B = 17 $$, substitute this back into the second equation to find $$ A $$:

$$ A = 2B + 9 $$
$$ A = 2(17) + 9 $$
$$ A = 34 + 9 $$
$$ A = 43 $$

**Conclusion:**
- **Ann has:** \$43
- **Betty has:** \$17
Ann has \$43 and Betty has \$17.

8. Ann and Betty together have \( \$ 60 \). Ann has \( \$ 9 \) more than twice Betty's amount. does each have? \[ 9 a+2 B=60 \]