Question

Tabitha is saving money for a new game. She already has $75 saved up. Every week, she add $12.50 to her savings. The game costs $195. How many weeks does Tabitha need to save before she has enough money to buy the game?

Answer 1

To determine how many weeks Tabitha needs to save, we can set up an equation based on her current savings, her weekly savings, and the cost of the game.

1. **Current Savings**: $75
2. **Weekly Savings**: $12.50
3. **Cost of the Game**: $195

We need to find how many weeks \( w \) it will take for her total savings to be at least $195. The equation for her total savings after \( w \) weeks can be represented as:

\[
75 + 12.50w \geq 195
\]

Now, we will solve for \( w \):

1. Subtract 75 from both sides:

\[
12.50w \geq 195 - 75
\]
\[
12.50w \geq 120
\]

2. Divide both sides by 12.50:

\[
w \geq \frac{120}{12.50}
\]
\[
w \geq 9.6
\]

Since \( w \) must be a whole number (she can’t save for a fraction of a week), we round up to the next whole number. Therefore, Tabitha needs to save for **10 weeks** to have enough money for the game.

To double-check:

- After 10 weeks, her total savings would be:

\[
75 + 12.50 \times 10 = 75 + 125 = 200
\]

Since $200 is greater than $195, Tabitha will have enough money after saving for **10 weeks**.