10. 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.

Question

10. 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.

Answer 1

Let x be the number of $1.50 items sold and y be the number of $3.50 items sold.

From the problem, we can set up two equations:
x + y = 150 (since there were initially 150 items)
1.5x + 3.5y = 227.5 (since the total earnings was $227.50)
Simplifying the first equation, we get:
x = 150 - y
Substituting this into the second equation, we get:
1.5(150 - y) + 3.5y = 227.5
Expanding and simplifying, we get:
225 - 1.5y + 3.5y = 227.5
2y = 2.5
y = 1.25
Since we cannot have sold a fraction of an item, we made an error in our calculations. Therefore, there is no solution that satisfies the given conditions.

Answer 2

Let's define the variables:

Let x be the number of items sold for $1.50.
Let y be the number of items sold for $3.50.

From the given information, we can establish two equations:

1. The total number of items sold: x + y = 150

2. The total amount earned: (1.50 * x) + (3.50 * y) = 227.50

These two equations create a system that can be solved to determine the values of x and y.

Answer 3

To solve this problem, we will create a system of equations based on the given information. Let's denote the number of items that cost $1.50 as 'x' and the number of items that cost $3.50 as 'y'.

1. We know that there were originally 150 items, so the first equation is:
x + y = 150

2. We also know that there are 41 items left, so the second equation is:
x + y = 41

3. We know the total amount of money collected ($227.50). Since each $1.50 item contributes $1.50 to the total and each $3.50 item contributes $3.50 to the total, the third equation is:
1.50x + 3.50y = 227.50

Now, we have a system of three equations that we can solve simultaneously to find the values of 'x' (number of items that cost $1.50) and 'y' (number of items that cost $3.50).