Kara and Lauri went shopping for some new summer clothes. They go to the same store and purchase some items. Kara buys 3 swimsuits and 2 pairs of shorts for $175. Lauri buys 2 swimsuits and 4 pairs of shorts for $170. Assume that all swimsuits are the same price and all shorts are the same price.
How would you determine how much one swimsuit costs? What about one pair of shorts? Try to find the two different prices in whatever way you can. Describe your process.
To determine how much one swimsuit costs, we can use the information given to create an equation. Since Kara and Lauri both bought the same items, we can assume that the price of the items is the same. We can set up the equation as follows:
3x + 2y = 175
2x + 4y = 170
We can then solve for x and y.
3x + 2y = 175
2x + 4y = 170
Subtracting the two equations:
x = 5
y = 25
Therefore, one swimsuit costs $5 and one pair of shorts costs $25.