28 and plain shirts cost $15. If she bought a total of 7 then how many of each kind did she buy?
The Correct Answer and Explanation is:
Let’s break down the problem using algebra.
Let:
- xxx represent the number of plain shirts she bought.
- yyy represent the number of 28 shirts she bought.
We know two things:
- The total number of shirts is 7, so: x+y=7x + y = 7x+y=7
- The total cost of the shirts is $15. Let’s assume that each plain shirt costs ppp and each 28-shirt costs qqq. The total cost is given by: p⋅x+q⋅y=15p \cdot x + q \cdot y = 15p⋅x+q⋅y=15 We need to assume the price for each shirt. Let’s assume a price for plain shirts, say, $2 per plain shirt, and $3 for the 28-shirt.
Using these values, the equation becomes:2x+3y=152x + 3y = 152x+3y=15
Now, we have the system of equations:
- x+y=7x + y = 7x+y=7
- 2x+3y=152x + 3y = 152x+3y=15
We can solve this system step-by-step:
Step 1: Solve the first equation for xxx:
x=7−yx = 7 – yx=7−y
Step 2: Substitute x=7−yx = 7 – yx=7−y into the second equation:
2(7−y)+3y=152(7 – y) + 3y = 152(7−y)+3y=1514−2y+3y=1514 – 2y + 3y = 1514−2y+3y=1514+y=1514 + y = 1514+y=15y=1y = 1y=1
Step 3: Find xxx:
Now substitute y=1y = 1y=1 into x=7−yx = 7 – yx=7−y:x=7−1=6x = 7 – 1 = 6x=7−1=6
Final Answer:
- She bought 6 plain shirts and 1 28-shirt.
Explanation:
To summarize, we set up a system of equations to represent the total number of shirts and the total cost. By substituting one equation into the other, we solved for the values of xxx (plain shirts) and yyy (28-shirts). This process gave us the number of each type of shirt she bought.
