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Question 1 of 3
1. Question
Greg earns `$20` per hour for the first `3` hours and `$15` per hour after that. How many hours should he work to earn `$135`?
(8) hours
Correct
Exceptional!
Incorrect
Help Video
Inverse Operations
When moving a term to the other side of an equation, the operation is inversed.
Keywords for Word Problems
Keyword
Meaning
Certain number
Unknown variable (`x,y,z,` etc)
is the same as, The answer is, is equal
`=`
sum, and, plus, more than
`+`
subtracted, less, minus
`-`
times, product, multiplied, twice
`times`
half of, divide by
`divide`
First, label the values and form an equation using the information given.
Extra hours needed to earn `$135=h`
`$20` per hour for `3` hours
and
`$15` per hour for the extra hours
should make
`$135`
`3(20)`
`+`
`15h`
`=`
`135`
Simplify the equation:
`3(20)+15h`
`=`
`135`
`60+15h`
`=`
`135`
To solve for `h`, it needs to be alone on one side.
Start by moving `60` to the other side by subtracting `60` from both sides of the equation.
`60+15``h`
`=`
`135`
`60+15``h``-60`
`=`
`135` `-60`
`15``h`
`=`
`75`
`60-60` cancels out
Next, remove `15` by dividing both sides of the equation by `15`.
`15``h`
`=`
`75`
`15``h``divide15`
`=`
`75``divide15`
`h`
`=`
`5`
`15divide15` cancels out
Add `h=5` to the first `3` hours.
Total hours needed
`=`
`3+``h`
`=`
`3+``5`
`=`
`5`
Greg needs to work `8` hours to earn `$135`.
`8` hours
Hint
Help Video
Question 2 of 3
2. Question
A set of `4` new tires and a `$90`-wheel alignment costs `$898` in total. How much does each tire cost?
`$`(202)
Correct
Fantastic!
Incorrect
Help Video
Inverse Operations
When moving a term to the other side of an equation, the operation is inversed.
Keywords for Word Problems
Keyword
Meaning
Certain number
Unknown variable (`x,y,z,` etc)
is the same as, The answer is, is equal
`=`
sum, and, plus, more than
`+`
subtracted, less, minus
`-`
times, product, multiplied, twice
`times`
half of, divide by
`divide`
First, label the values and form an equation using the information given.
Cost of each tire`=t`
`4` tires
and
a `$90`-wheel alignment
costs
`$898`
`4t`
`+`
`90`
`=`
`898`
To solve for `t`, it needs to be alone on one side.
Start by moving `90` to the other side by subtracting `90` from both sides of the equation.
`4``t` `+90`
`=`
`898`
`4``t` `+90` `-90`
`=`
`898` `-90`
`4``t`
`=`
`808`
`90-90` cancels out
Next, remove `4` by dividing both sides of the equation by `4`.
`4``t`
`=`
`808`
`4``t``divide4`
`=`
`808``divide4`
`t`
`=`
`$202`
`4divide4` cancels out
Each tire costs `$202`.
`$202`
Hint
Help Video
Question 3 of 3
3. Question
A hire car costs `$95` per day plus `80¢` per kilometre it is driven. If the total cost of hiring the car was `$175`, how many kilometres was it driven?
(100) kilometres
Correct
Good Job!
Incorrect
Help Video
Inverse Operations
When moving a term to the other side of an equation, the operation is inversed.
Keywords for Word Problems
Keyword
Meaning
Certain number
Unknown variable (`x,y,z,` etc)
is the same as, The answer is, is equal
`=`
sum, and, plus, more than
`+`
subtracted, less, minus
`-`
times, product, multiplied, twice
`times`
half of, divide by
`divide`
First, make sure all units are the same. Convert the cents to dollars knowing that `$1=100¢`.
Cost of each kilometre the car is driven
`=`
`80¢`
`=`
`80¢divide100¢`
`=`
`$0.8`
Now, label the values and form an equation using the information given.
Number of kilometres driven`=x`
A hire car costs `$95` per day
plus
`80¢` per kilometre.
The total cost of hiring the car was
`$175`
`95`
`+`
`0.8x`
`=`
`175`
To solve for `x`, it needs to be alone on one side.
Start by moving `95` to the other side by subtracting `95` from both sides of the equation.
`95+0.8``x`
`=`
`175`
`95+0.8``x``-95`
`=`
`175` `-95`
`0.8``x`
`=`
`80`
`95-95` cancels out
Next, remove `0.8` by dividing both sides of the equation by `0.8`.
