Find out how much Grace earned if she earned $27 more than Robert and Alexis combined. Alexis worked 3 hours more than Robert and 7 hours less than Grace.
Robert earned $7.50/hr, Alexis earned $6/hr, Grace earned $9/hr
How much did Grace earn?
Find out how much Grace earned if she earned $27 more than Robert and Alexis combined. Alexis worked 3 hours more than Robert and 7 hours less than Grace.
Robert earned $7.50/hr, Alexis earned $6/hr, Grace earned $9/hr
How much did Grace earn?
Make a lot of different equations and piece together to solve for one variable at a time.
g = Grace hours $9.00g = what Grace earns per g hours
r = Robert hours $7.50r = what Robert earns per r hours
a = Alexis hours $6.00a = what Alexis earns per a hours
Grace earned if she earned $27 more than Robert and Alexis combined
because earned, we need to use the equations above that have the money involved per hour
$9.00g = ($7.50r + $6.00a) + $27.00
Alexis worked 3 hours more than Robert
because this is just hours, no money in equation
a = r + 3 OR r = a - 3
Alexis worked 7 hours less than Grace.
a = g - 7 OR g = a + 7
Put the equations together to help you get to only have a's in one equation, and solve for a
$9.00g = ($7.50r + $6.00a) + $27.00
$9.00(a + 7) = ($7.50(a - 3) + $6.00a) + $27.00
$9.00a + $63.00 = $7.50a - $22.50 + $6.00a + $27.00
-$4.50a = -$58.50
a = 13
Plug a back into previous equations to solve for g and r
g = a + 7 = (13) + 7 = 20
r = a - 3 = (13) - 3 = 10
It asked how much Grace earned, not how many hours, so take your answer for g and plug into her hourly equation
$9.00g
$9.00(20)
$180.00
Hi,
I would approach word problems starting with the 'least' or lowest' and add on others in relation to it.
What is asked ?
Grace's earning
What is given ?
relationship between her earning and those of (Robert and Alexis)
relationship between Robert and Alexis earning
rates of earning of all 3
=> there are two things here : no of hours and rate ; earning depends upon both
Starting from lowest,
Let X be the number of hours Robert worked (his rate is known $7.50 per hour)
Robert earned $7.5X
Then Alexis worked X + 3 hours (his rate is known also $6 per hour)
Alexis earned (X+3)*6 =$(6X + 18)
Therefore Alexis and Robert together earned : 7.5X + 6X + 18 = 13.5X + 18
Now Grace earned 27$ more than both Robert and Alexis together, so add 27$ to their total
So Grace earned 13.5X + 18 + 27 = $(13.5X + 45)
If we can find out what X is, we will know Grace's earning. (the solution we need)
So number of hours Grace worked is total earnings / rate per hour = (13.5X +45) / 9
But we know that Alexis worked 7 hours less than Grace so
So number of hours worked by Alexis is {(13.5X + 45) / 9 } - 7
But Alexis also worked 3 hours more than Robert. So we can equate them
X + 3 = {(13.5X + 45) / 9} - 7
Solve the equation for X as follows :
X + 3 = (13.5X/9) + (45/9) - 7
X + 3 = (13.5X/9) + 5 - 7
X = (13.5X/9) + 5 - 7 -3 (subtracting 3 from both sides)
X = (13.5X/9) - 5
9X = (13.5X) - (5 * 9) (multiplying both sides by 9 to ease solving)
9X - 13.5X = -45 (subtracting 13.5X from both sides)
-4.5X = - 45
X = 45/4.5 (multiplying both sides by -1)
X = 10 hours
Therefore Grace earned (remember it was $(13.5X + 45))
(13.5*10) + 45 = 135 + 45 = 180$
verify that 180$ is 27 more than Alexis and Robert earnings put together!
Hope this helps!