Question

Bill and Mary Ann went to the Viola bakery. Bill bought 4 cookies and 9 donuts for ​$14.78. Mary Ann bought 6 of each for ​$12.42. What is the price of each type of​ treat

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Answer 1

The price of a cookie is $0.77 and the price of a donut is $1.30.

Step-by-step explanation:

To solve this problem, we can set up a system of equations. Let's represent the price of a cookie as C and the price of a donut as D. From the information given, we can create the following equations:

1. 4C + 9D = 14.78 (equation 1)
2. 6C + 6D = 12.42 (equation 2)

Now, we can solve this system of equations using any method, such as substitution or elimination. Let's use the elimination method:

1. Multiply equation 2 by 2:
2. 12C + 12D = 24.84
3. Subtract equation 1 from equation 2:
4. 12C + 12D - (4C + 9D) = 24.84 - 14.78
5. 8C + 3D = 10.06 (equation 3)
6. Multiply equation 1 by 3:
7. 12C + 27D = 44.34
8. Subtract equation 3 from equation 1:
9. 12C + 27D - (8C + 3D) = 44.34 - 10.06
10. 4C + 24D = 34.28
11. Divide equation 4 by 4:
12. C + 6D = 8.57 (equation 4)
13. Substitute the value of C from equation 4 into equation 3:
14. 8(8.57 - 6D) + 3D = 10.06
15. 68.56 - 48D + 3D = 10.06
16. -45D = -58.5
17. D = 1.3
18. Substitute the value of D into equation 4:
19. C + 6(1.3) = 8.57
20. C + 7.8 = 8.57
21. C = 0.77

Therefore, the price of a cookie is $0.77 and the price of a donut is $1.30.