QuestionBen is saving money to buy an Xbox One $S$ that costs $\$ 323$ including tax. He opens a savings account with a deposit of $\$ 75$ and deposits $\$ 55$ each week after mowing lawns. What is the minimum number of weeks Ben will need to make deposits until he has enough money in his account to buy the Xbox?
Ben will have enough money to pay for the Xbox after at least weeks.
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Studdy Solution
Solve the inequality for the number of weeks.
Subtract 75 from both sides to isolate the term with $w$:
$$55w \geq 323 - 75$$ $$55w \geq 248$$
Divide both sides by 55 to solve for $w$:
$$w \geq \frac{248}{55}$$ $$w \geq 4.509$$
Since $w$ must be a whole number (as Ben cannot work a fraction of a week), round up to the nearest whole number:
$w = 5$
Ben will need to deposit money for at least $\boxed{5}$ weeks to have enough to buy the Xbox.