kayla spends $48 on gym clothes. she buys at least of each item. shorts cost $16, t-shirt cost $18 and socks cost $2 a pair how many ways can kayla spend $48 on her gym clothes
You left out a word.
She buys at least ___ of an item.
four.
she buys at least one of them right? well. then she can do it in four ways
To find out the number of ways Kayla can spend $48 on gym clothes, we can use a combination of techniques such as equations and reasoning.
Let's denote the number of shorts she buys as S, the number of t-shirts as T, and the number of pairs of socks as P. Given that she buys at least one of each item, we have the following constraints:
Cost of shorts: 16S
Cost of t-shirts: 18T
Cost of socks: 2P
And since she spends a total of $48, we can create an equation:
16S + 18T + 2P = 48
Now, since all variables need to be at least one, we can try different values for S, T, and P while satisfying the equation.
Starting with S = 1, we can substitute it into the equation and find a solution for T and P that satisfies the equation. Then we increase S by one and repeat the process until we no longer find suitable solutions.
Let's go through the process step-by-step:
1. S = 1:
- Substitute S = 1 into the equation: 16(1) + 18T + 2P = 48
- Simplify the equation: 34 + 18T + 2P = 48
- Rearrange the equation: 18T + 2P = 14
- We can see that T = 0 and P = 7 is a valid solution.
- So, when S = 1, there is one possible combination: (1 short, 0 t-shirts, 7 pairs of socks).
2. S = 2:
- Substitute S = 2 into the equation: 16(2) + 18T + 2P = 48
- Simplify the equation: 32 + 18T + 2P = 48
- Rearrange the equation: 18T + 2P = 16
- We can see that T = 0 and P = 8 is a valid solution.
- So, when S = 2, there is one possible combination: (2 shorts, 0 t-shirts, 8 pairs of socks).
3. S = 3:
- Substitute S = 3 into the equation: 16(3) + 18T + 2P = 48
- Simplify the equation: 48 + 18T + 2P = 48
- Rearrange the equation: 18T + 2P = 0
- There are no valid solutions for T and P since 2P can never be equal to 0.
- Therefore, there are no possible combinations when S = 3 or higher.
In conclusion, there are two possible combinations for Kayla to spend $48 on her gym clothes:
1. (1 short, 0 t-shirts, 7 pairs of socks)
2. (2 shorts, 0 t-shirts, 8 pairs of socks)
Please note that there may be other possible combinations if we allow her to buy more t-shirts or have a different distribution of items.