Real world systems of equations practice
1. A store sells two types of oranges, type A and type B. Type A oranges cost $0.50 each, and type B oranges cost $0.75 each. If a customer buys 10 oranges for a total of $6.50, how many of each type of orange did they purchase?
Let x be the number of type A oranges purchased, and y be the number of type B oranges purchased.
The equations can be set up as:
x + y = 10 (total number of oranges purchased)
0.50x + 0.75y = 6.50 (total cost of the oranges purchased)
Solving these equations simultaneously will give us the values of x and y.
2. The revenue (R) of a company is given by the equation R = 500x + 300y, where x is the number of product A sold and y is the number of product B sold. The company sold a total of 100 products and made $25,000 in revenue. If the revenue from product A is twice as much as the revenue from product B, how many of each product were sold?
Let x be the number of product A sold, and y be the number of product B sold.
The equations can be set up as:
x + y = 100 (total number of products sold)
500x + 300y = 25000 (total revenue)
Since the revenue from product A is twice the revenue from product B, we have the additional equation:
500x = 2(300y)
Solving these equations simultaneously will give us the values of x and y.
3. A packaging company sells two types of boxes, small and large. The price of a small box is $5, and the price of a large box is $8. If the company sells a total of 50 boxes for $300, how many of each type of box were sold?
Let x be the number of small boxes sold, and y be the number of large boxes sold.
The equations can be set up as:
x + y = 50 (total number of boxes sold)
5x + 8y = 300 (total revenue from the boxes)
Solving these equations simultaneously will give us the values of x and y.