Question
Three friends, Mackenzie, Enola, and Shandra are saving different amounts of money each week. Mackenzie started with 18 and added 10 every week. Enola's savings are represented by the table below, and Shandra's savings are represented by the graph below. Enola's Savings Weeks (x) & Total Savings (y) 2 & 54 6 & 134 10 & 214 14 & 294
Solution
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Tatum
Master ยท Tutor for 5 years
Answer
To compare the savings of Mackenzie, Enola, and Shandra, we need to determine the rate at which each of them is saving money per week and their starting amount. We already have this information for Mackenzie, so we need to calculate it for Enola and Shandra.Step 1: Calculate Enola's weekly savings rate and starting amount.From Enola's savings table, we can see that her savings increase by the same amount every four weeks. We can calculate the weekly savings rate by taking the difference between any two consecutive savings amounts and dividing by the number of weeks between them.For example, between weeks 2 and 6, Enola's savings increased by:
54 =
80 / 4 weeks =
54 - (2 weeks *
54 -
14So, Enola started with
20 every week.Step 2: Calculate Shandra's weekly savings rate and starting amount using the graph.We have two points from Shandra's savings graph: (5,
144). We can use these points to find the slope of the line, which represents Shandra's weekly savings rate.The slope (m) is calculated by the change in y divided by the change in x:m = (y2 - y1) / (x2 - x1)Using the points (5,
144):m = (
91.50) / (8 - 5)m =
17.50 per weekThis means Shandra saves
91.50):
17.50(5 - x1)Since we want to find the starting amount, we set x1 to 0 (the starting week):
17.50(5 - 0)
87.50y1 =
87.50y1 =
4 and adds
18 and adds
14 and adds
4 and adds $17.50 every week.