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Difficulty:
15%
(low)
Question Stats:
87% (00:55) correct
12% (03:09) wrong based on 8 sessions
History
Date
Time
Result
Not Attempted Yet
Ann’s tree is 76 inches tall and is growing at a rate of 3.6 inches per year. Bob’s tree is 58 inches tall and is growing at a rate of 4.8 inches per year. In how many years will Bob’s tree reach Ann’s tree in height?
A. 12
B. 14
C. 15
D. 20
E. 25
A. 12
B. 14
C. 15
D. 20
E. 25
16 Aug 2025, 03:17
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Official Explanation
Set up a linear equation to model each tree’s growth. Let x be the number of years, and let y, the dependent variable, represent the height of the tree as it varies over time. For Ann’s tree, \(y = 3.6 x + 76;\) for Bob’s, \(y = 4.8 x + 58.\) When the trees’ heights are equal, the y values in each equation will be equal, so we can set \(3.6 x + 76\) equal to \(4.8 x + 58.\) Then, group like terms together by subtracting 3.6 x and 58 from both sides: Finally, divide both sides by 1.2 to obtain x = 15, (C).
Answer: C
Set up a linear equation to model each tree’s growth. Let x be the number of years, and let y, the dependent variable, represent the height of the tree as it varies over time. For Ann’s tree, \(y = 3.6 x + 76;\) for Bob’s, \(y = 4.8 x + 58.\) When the trees’ heights are equal, the y values in each equation will be equal, so we can set \(3.6 x + 76\) equal to \(4.8 x + 58.\) Then, group like terms together by subtracting 3.6 x and 58 from both sides: Finally, divide both sides by 1.2 to obtain x = 15, (C).
Answer: C
