Question
Tadeo volunteered at the library 6 times as many hours over the weekend as Dylan. Together, they volunteered a total of 14 hours. How many hours did each person volunteer over the weekend?
Ask by Parry Pollard. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Dylan volunteered 2 hours and Tadeo volunteered 12 hours over the weekend.
Solution
Let Dylan's hours be D and Tadeo's hours be T. According to the problem, Tadeo volunteered 6 times as many hours as Dylan, so we have:
T = 6D
We also know that together they volunteered a total of 14 hours:
T + D = 14
Substitute T = 6D into the equation:
6D + D = 14
7D = 14
Divide both sides by 7:
D = 2
Now, substitute D back into T = 6D:
T = 6 × 2 = 12
So, Dylan volunteered 2 hours and Tadeo volunteered 12 hours over the weekend.
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Simplify this solution The Deep Dive
Let's break this down into an equation. If we let Dylan's hours be represented by \( x \), then Tadeo's hours would be \( 6x \) since he volunteered 6 times as many hours. Together, they volunteered a total of 14 hours, which gives us the equation: \[ x + 6x = 14 \] Combine like terms: \[ 7x = 14 \] Now, divide both sides by 7: \[ x = 2 \] So, Dylan volunteered 2 hours, and Tadeo, volunteering 6 times that, worked \( 6 \times 2 = 12 \) hours. Therefore, Dylan volunteered 2 hours, and Tadeo volunteered 12 hours!
