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Question 1 of 2
1. Question
`4` T-shirts and `5` hats cost `$92` altogether. If a T-shirt costs `$5` more than a hat, find the cost of each item.-
T-shirt`=$` (13)Hat`=$` (8)
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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` T-shirt`=$13`Hat`=$8` -
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Question 2 of 2
2. Question
The cost of two different cereal boxes differs by `$1.10`. If their total cost is `$8.90`, what is the cost of the more expensive cereal box?- `$` (5)
Hint
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Good Job!
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` Simplify the equation:`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`.`$5`
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