Question

Your mother has left you in charge of the annual family yard sale. Before she leaves you to your entrepreneurial abilities, she explains that she has made the job easy for you: everything costs either $1.50 or $3.50. She asks you to keep track of how many of each type of item is sold, and you make a list, but it gets lost sometime throughout the day. Just before she’s supposed to get home, you realize that all you know is that there were 150 items to start with (your mom counted) and you have 41 items left. Also, you know that you made $227.50. Write a system of equations that you could solve to figure out how many of each type of item you sold.

A) x + y = 109
(1.5)x + 227.50 = (3.5)y
B) x + y = 109
(3.5)x + 227.50 = (1.5)y
C) x + y = 41
(1.5)x + 227.50 = (3.5)y
D) x + y = 109
(1.5)x + (3.5)y = 227.50
E) x + y = 150
(1.5)x + (3.5)y = 227.50
F) x + y = $3.50
(1.5)x + (3.5)y = 227.50

Answer 1

`D)\ x + y = 109\\(1.5)x + (3.5)y = 227.50`

Explanation:

Let the items sold with price $1.5 =
`x`

Let the items sold with price $3.5 =
`y`

Initially, total number of items = 150

Items left at the end of the day = 41

So, number of items sold throughout the day = Total number of items - Number of items left

Number of Items sold = 150 - 41 = 109

So, the first equation can be written as:

`\bold{x+y = 109} ....... (1)`

Now, let us calculate the sales done by each item.

Sales from item with price $1.5 = Number of items sold
`*` price of each item

= (1.5)
`x`

Sales from item with price $3.5 = Number of items sold
`*` price of each item

= (3.5)
`y`

Total sales =
`\bold{(1.5)x+(3.5)y = 227.50} ....... (2)`

So, the correct answer is:

`D)\ x + y = 109\\(1.5)x + (3.5)y = 227.50`