Question

Emily noticed that on halloween, her child got three basic types of candy: chocolate, gummy, and hard candy. She has 15 more hard candies that chocolate, and 5 less than twice the amount for gummy candy than chocolate. if she had a total of 178 pieces of candy, how many of each type did she get?

Answer 1

Answer: gotta scroll down sry

Explanation:

First set up equations with variables that show the information you have:
c = chocolate // g = gummy // h = hard candy

178 = c + g + h

h = c + 15

g = 2c - 5

Then, solve all the equations for a number:

178 = c + g + h (leave as is)

15 = -c + h (subtract 'c' from the original equation's right side and switch the sides of the equation)

-5 = -2c + g (subtract '2c' from the original equation's right side and switch the side of the equation)

Then, line up all the variables and subtract the top equation by the lower two:

178 = c + g + h

15 = -c + 0g + h

-5 = -2c + g + 0h

---------------------------

168 = 4c + 0g + 0h >>>> 168 = 4c

Solve for 'c' and plug it into the other equations to find 'h' and 'g':

168/4 = 4c/4

42 = c

15 = -(42) + h -5 = -2(42) +g

57 = h 79 = g

Add all the numbers together to double-check:

42 + 57 + 79 = 178

chocolates = 42

gummies = 79

hard candies = 57