Rosita and Garth are saving up for a vacation, and begin with a certain amount saved each. If Rosita works 5 hours, she will have $128. If she works 7 hours, she will have $164. If Garth works 3 hours, he will have $124. If he works 8 hours, he will have $194. They want to know when they will have saved the same amount of money and how much each will have saved.

Question

Mathematics

Steve Mckenzie

3 October, 16:10

Rosita and Garth are saving up for a vacation, and begin with a certain amount saved each. If Rosita works 5 hours, she will have $128. If she works 7 hours, she will have $164. If Garth works 3 hours, he will have $124. If he works 8 hours, he will have $194. They want to know when they will have saved the same amount of money and how much each will have saved.

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Answers (1)

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Madalyn Pineda · Answer 1

Treat each (time, money) pair as an (x, y) pair, and get the slope of the line:

For Rosita, (5, 128), (7, 164) : m = (y2 - y1) / (x2 - x1) = (164 - 128) / (7 - 5) = 18, implying that she earns $18/hr. The y-intercept is calculated as: y = 18x + b, 128 = 18*5 + b, b = $38, meaning that she started with $38. Rosita's equation is y = 18x + 38.

For Garth, (3, 124), (8, 194) : m = (194 - 124) / (8 - 3) = 14. For 124 = 14*3 + b, b = $82. Garth's equation is y = 14x + 82

To find out when they will have saved the same amount, both equations would have the same y-value:

18x + 38 = 14x + 82

4x = 44

x = 11 hours

y = 18*11 + 38 = $236 (alternatively, y = 14*11 + 82 = 236)

This means that Rosita and Garth will have both saved $236 after 11 hours of working.