Question

You go to the store and buy x bags of carrots and y bananas. Each bag of carrots costs $1.50 and each banana is $0.25. You spend $6.50. The total number of items you purchase is 11. How many bags of carrots did you buy? How many bananas did you buy?

a) Bags of carrots (x) = 4, Bananas (y) = 7
b) Bags of carrots (x) = 3, Bananas (y) = 8
c) Bags of carrots (x) = 5, Bananas (y) = 6
d) Bags of carrots (x) = 2, Bananas (y) = 9

Answer 1

After setting up and solving a system of linear equations, it is determined that 4 bags of carrots and 7 bananas were purchased, which corresponds to the first option given in the multiple-choice answers.

Step-by-step explanation:

The problem presents a system of linear equations we can use to determine how many bags of carrots and bananas were purchased. The first equation represents the total cost, and the second equation represents the total number of items bought. To set up the equations, we use the given prices: $1.50 per bag of carrots and $0.25 per banana. The total spent on these items is $6.50, and the total number of items is 11.

The equations based on the given information are:

1. 
   
3. 
   

We can solve this system of equations using either substitution or elimination method. Let's use substitution by expressing y in terms of x from the second equation:

1. 
   
3. y = 11 - x

Now we substitute y in the total cost equation:

1.50x + 0.25(11 - x) = 6.50

By solving this equation, we find that x = 4 (bags of carrots) and y = 7 (bananas), which corresponds to option (a)