HELP! How do I set this problem up? Im confuzzled...
Tom mows lawns and whitewashes fences during his summer vacation. He is paid $12 for each lawn mowed and $17 for each fence painted. Last month Tom did 105 jobs and made a total of $1410. How many of each job did he do?
12L + 17 F = 1410
L + F = 105
I hope this helps
Sharon earns $30 for each lawn she mows
To solve this problem, let's set up a system of equations. Let's assume Tom mowed x lawns and painted y fences.
According to the given information:
1. Tom is paid $12 for each lawn mowed, so the total amount earned from mowing lawns is 12x.
2. Tom is paid $17 for each fence painted, so the total amount earned from painting fences is 17y.
3. Last month, Tom did 105 jobs, which gives us the equation x + y = 105.
4. The total amount Tom made from all the jobs is $1410, so we have the equation 12x + 17y = 1410.
Now we have a system of equations:
x + y = 105 (Equation 1)
12x + 17y = 1410 (Equation 2)
To solve this system, we can use substitution or elimination.
Method 1: Substitution
Since Equation 1 is already solved for x, we can substitute this value of x into Equation 2:
12(105 - y) + 17y = 1410
Simplifying:
1260 - 12y + 17y = 1410
5y = 150
y = 30
Now that we know y = 30, we can substitute this value into Equation 1 to find x:
x + 30 = 105
x = 105 - 30
x = 75
Therefore, Tom mowed 75 lawns and painted 30 fences.
Method 2: Elimination
Multiply Equation 1 by 12 to make the coefficient of x the same in both equations:
12x + 12y = 1260 (Equation 3)
Now subtract Equation 3 from Equation 2 to eliminate x:
12x + 17y - (12x + 12y) = 1410 - 1260
5y = 150
y = 30
Substitute the value of y back into Equation 1:
x + 30 = 105
x = 105 - 30
x = 75
Thus, Tom mowed 75 lawns and painted 30 fences.
Either method will give you the same result.