Solving a fraction word problem using a linear equation of the form
Henry is saving money to buy a game. So far he has saved , which is three-fourths of the total cost of the game. How much does the game cost?

Question

Solving a fraction word problem using a linear equation of the form

Henry is saving money to buy a game. So far he has saved

, which is three-fourths of the total cost of the game. How much does the game cost?

UpStudy AI · Accepted Answer

To determine the total cost of the game that Henry is saving for, we can set up and solve a linear equation of the form $$ A x = B $$.

### Step 1: Define the Variable
Let:
- $$ x $$ = Total cost of the game in dollars.

### Step 2: Set Up the Equation
According to the problem, Henry has saved \$12, which is three-fourths ($$ \frac{3}{4} $$) of the total cost of the game. This relationship can be expressed as:
$$
\frac{3}{4}x = 12
$$
Here:
- $$ A = \frac{3}{4} $$
- $$ B = 12 $$

### Step 3: Solve for $$ x $$
To isolate $$ x $$, follow these steps:

1. **Multiply both sides by the reciprocal of $$ \frac{3}{4} $$ to get $$ x $$ by itself. The reciprocal of $$ \frac{3}{4} $$ is $$ \frac{4}{3} $$.**
$$
x = 12 \times \frac{4}{3}
$$

2. **Perform the multiplication:**
$$
x = 12 \times \frac{4}{3} = \frac{48}{3} = 16
$$

### Step 4: Interpret the Solution
The total cost of the game is:
$$
x = \$16
$$

### Conclusion
Henry needs to save a total of **\$16** to purchase the game.
The game costs \$16.

Solving a fraction word problem using a linear equation of the form
Henry is saving money to buy a game. So far he has saved , which is three-fourths of the total cost of the game. How much does the game cost?

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