Sam currently has $50 in savings. He had been saving $8 each week. Yesterday he spent $142 of the savings. For how many weeks had he been saving? (a) Write an equation that could b... Sam currently has $50 in savings. He had been saving $8 each week. Yesterday he spent $142 of the savings. For how many weeks had he been saving? (a) Write an equation that could be used to answer the question above. First, choose the appropriate form. Then, fill in the blanks with the numbers 50, 8, and 142. Let w represent the number of weeks. w + = w - = (b) Solve the equation in part (a) to find the number of weeks. w =
Understand the Problem
The problem describes a scenario where Sam has initial savings and saves a fixed amount each week. Then, he spends a certain amount from his total savings and we are required to figure out how many weeks he has been saving. Part (a) involves creating an equation using the given numbers to represent this scenario, letting 'w' represent the number of weeks. Part (b) asks to solve the equation formulated in part (a) to find the value of 'w'.
Answer
(a) $8w + 50 = 142$ (b) $w = 11.5$
Answer for screen readers
(a) $8w + 50 = 142$ (b) $w = 11.5$
Steps to Solve
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Set up the equation The total saved can be represented as the initial savings plus the savings per week times the number of weeks. Since Sam spent $142, we know the total savings must be at least $142. The equation will be in the form: savings per week * number of weeks + initial savings = total spent. $8w + 50 = 142$
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Solve for w Subtract 50 from both sides of the equation: $8w + 50 - 50 = 142 - 50$ $8w = 92$
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Isolate w Divide both sides by 8: $\frac{8w}{8} = \frac{92}{8}$ $w = 11.5$
(a) $8w + 50 = 142$ (b) $w = 11.5$
More Information
The answer $w = 11.5$ means that Sam had been saving for 11 and a half weeks.
Tips
A common mistake is to set up the equation incorrectly, for example, using subtraction instead of addition or misplacing the numbers in the equation. Also, an alternative, yet perfectly acceptable answer would be to round the number of weeks to 12.
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