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Our variables represent the number of each kind of gift card purchased.
Equation in Standard Form: 10x+25y=285
Example Solutions: See solution.
We are told that gift cards can be purchased for $10 or for $25. We want to know how many of each kind we could have purchased when spending $285.
We need to find three combinations for the numbers of each card purchased that fit our equation. These numbers need to be whole numbers because we cannot purchase a portion of a gift card. The best method here is to guess and check. But, we can make educated guesses! We have some things to consider when making these educated guesses.
y | 10x+25y=285 | x |
---|---|---|
3 | 10x+25* 3=285 | 21 |
5 | 10x+25* 5=285 | 16 |
This means that if we bought 5 $25 gift cards, we also bought 16 $10 gift cards. While there are more possibilities, three example combinations are as follows.
The Number of $25 Gift Cards | The Number of $10 Gift Cards |
---|---|
1 | 26 |
3 | 21 |
5 | 16 |