SOLUTION: 1. one number is 5 more than 3 times another number. The sum of the two numbers is 157. Find the bigger number. 2. Robert can paint a room in 12 hours. His helper can do the same

Question 272114: 1. one number is 5 more than 3 times another number. The sum of the two numbers is 157. Find the bigger number.
2. Robert can paint a room in 12 hours. His helper can do the same work in 24 hours. How long will it take them to paint the room together?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1. one number is 5 more than 3 times another number. The sum of the two numbers is 157. Find the bigger number.
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a = 3b + 5
a + b = 157
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Substitute for "a" and solve for "b":
3b + 5 + b = 157
4b + 5 = 157
4b = 152
b = 38
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Since a = 3b+5, a = 3*38+5 = 119
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2. Robert can paint a room in 12 hours. His helper can do the same work in 24 hours. How long will it take them to paint the room together?
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Robert rate = 1/12 job/hr/
Helper rate = 1/24 job/hr
Together rate = 1/x job hr
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Equation:
rate + rate = together rate
1/12 + 1/24 = 1/x
Multiply thru by 24x to get:
2x + x = 24
3x = 24
x = 8 hrs (time to do the job together)
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Cheers,
Stan H.

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