Question

Mrs Rivera goes to a local grocery store to buy trail mix ingredients for a hiking trip. The store sells bags of mixed nuts for $1.49 and bags of dried fruit for $.99. Her receipt shows that she bought 17 items for $22.83. How many of each did she buy?

Please show your work!

Answer 1

Let's use a system of equations to solve the problem.

Let x be the number of bags of mixed nuts and y be the number of bags of dried fruit that Mrs. Rivera bought. We know that she bought a total of 17 items, so:

x + y = 17 ... (equation 1)

We also know that the total cost of her purchase was $22.83, so:

1.49x + 0.99y = 22.83 ... (equation 2)

To solve for x and y, we can use equation 1 to solve for one variable in terms of the other. Solving for y, we get:

y = 17 - x

Substituting this expression for y into equation 2, we get:

1.49x + 0.99(17 - x) = 22.83

Simplifying and solving for x, we get:

1.49x + 16.83 - 0.99x = 22.83

0.50x = 6.00

x = 12

So Mrs. Rivera bought 12 bags of mixed nuts. Substituting this value into equation 1 to solve for y, we get:

12 + y = 17

y = 5

Therefore, Mrs. Rivera bought 12 bags of mixed nuts and 5 bags of dried fruit.