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Question 1 of 2
`4` T-shirts and `5` hats cost `$92` altogether. If a T-shirt costs `$5` more than a hat, find the cost of each item.
Incorrect
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.
T-shirt`=x`
Hat`=x-5` (since a T-shirt costs `$5` more)
Total Cost `=$92`
| `4` T-shirts |
and |
`5` Hats |
cost |
`$92` |
| `4x` |
`+` |
`5(x-5)` |
`=` |
`92` |
To solve for `x`, it needs to be alone on one side.
Start by expanding the left side of the equation by using the Distributive Property.
| `4``x` `+``5``(``x` `-5)` |
`=` |
`92` |
| `4``x` `+``5``x` `-``5``(5)` |
`=` |
`92` |
| `4``x` `+5``x` `-25` |
`=` |
`92` |
| `9``x` `-25` |
`=` |
`92` |
Next, move `-25` to the other side by adding `25` to both sides of the equation.
| `9``x` `-25` |
`=` |
`92` |
| `9``x` `-25` `+25` |
`=` |
`92` `+25` |
| `9``x` |
`=` |
`117` |
`-25+25` cancels out |
Remove `9` by dividing both sides of the equation by `9`.
| `9``x` |
`=` |
`117` |
| `9``x``divide9` |
`=` |
`117``divide9` |
| `x` |
`=` |
`13` |
`9divide9` cancels out |
Substitute `x=13` to get the cost of each T-shirt and hat.
| T-shirt |
`=` |
`x` |
|
`=` |
`$``13` |
| Hat |
`=` |
`x` `-5` |
|
`=` |
`13` `-5` |
|
`=` |
`$8` |
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Question 2 of 2
The cost of two different cereal boxes differs by `$1.10`. If their total cost is `$8.90`, what is the cost of the more expensive cereal box?
Incorrect
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.
Use cents (`¢`) for easier computation.
More expensive cereal`=x`
Cheaper cereal`=x-110` (since it is `$1.10` or `110¢` cheaper)
Total Cost `=$8.90=890¢`
| The more expensive cereal |
and |
the cheaper cereal |
cost |
`$8.90` |
| `x` |
`+` |
`x-110` |
`=` |
`890` |
| `x+x-110` |
`=` |
`890` |
| `2x-110` |
`=` |
`890` |
To solve for `x`, it needs to be alone on one side.
Start by moving `-110` to the other side by adding `110` to both sides of the equation.
| `2x-110` |
`=` |
`890` |
| `2x-110` `+110` |
`=` |
`890` `+110` |
| `2``x` |
`=` |
`1000` |
`-110+110` cancels out |
Next, remove `2` by dividing both sides of the equation by `2`.
| `2``x` |
`=` |
`1000` |
| `2``x``divide2` |
`=` |
`1000``divide2` |
| `x` |
`=` |
`500¢` |
`2divide2` cancels out |
| `x` |
`=` |
`$5` |
Convert unit to dollars |
Since `x` is the more expensive cereal box, its cost is `$5`.
