Tom got paid $39.00 for weeding his neighbor's garden 7 times. He got paid 5 dollars if done in less than a hour and 6 dollars if done more than a hour. How many times did he take more than an hour...

Tom got paid $39.00 for weeding his neighbor's garden 7 times. He got paid 5 dollars if done in less than a hour and 6 dollars if done more than a hour.

How many times did he take more than an hour to weed.

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steveschoen | College Teacher | (Level 1) Associate Educator

Posted on

Hi, homework4541.  I hope this will assist.

We can solve this by systems of equations.  We can make:

x = # times less than an hour

y = # times more than an hour

(we will assume nothing at exactly one hour)

These have to total 7 times.  So:

x+y = 7

Then, for less than a hour, we get paid $5 each time.  That means we got a total of 5x dollars, 5 times the number of times we weeded the garden in less than an hour.  Similarly, we get paid 6y total for taking more than an hour.  These have to total $39.  So:

5x + 6y = 39

So, we have:

x+y = 7

5x + 6y = 39

Various ways to solve these from here.  I would multiply the first equation by 6, giving us:

6x + 6y = 42

5x + 6y = 39

Subtracting the second equation from the first equation, we get:

x = 3

So, we weeded the garden in less than an hour 3 times.  But, going back to check, we are looking for y, the number of times we took more than an hour.  Since:

x+y = 7

And, x = 3, then:

3+y = 7

y = 4

So, we weeded the garden 4 times in more than an hour.  That's our answer.

I hope this helps, homework4541.  Good luck.

Steve

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