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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.
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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 |
× |
half of, divide by |
÷ |
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.
4x +5(x -5) |
= |
92 |
4x +5x -5(5) |
= |
92 |
4x +5x -25 |
= |
92 |
9x -25 |
= |
92 |
Next, move -25 to the other side by adding 25 to both sides of the equation.
9x -25 |
= |
92 |
9x -25 +25 |
= |
92 +25 |
9x |
= |
117 |
-25+25 cancels out |
Remove 9 by dividing both sides of the equation by 9.
9x |
= |
117 |
9x÷9 |
= |
117÷9 |
x |
= |
13 |
9÷9 cancels out |
Substitute x=13 to get the cost of each T-shirt and hat.
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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
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0:00
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 |
× |
half of, divide by |
÷ |
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 |
2x |
= |
1000 |
-110+110 cancels out |
Next, remove 2 by dividing both sides of the equation by 2.
2x |
= |
1000 |
2x÷2 |
= |
1000÷2 |
x |
= |
500¢ |
2÷2 cancels out |
x |
= |
$5 |
Convert unit to dollars |
Since x is the more expensive cereal box, its cost is $5.