Question

A candy maker makes two sizes of candies. Using the smaller size, a full jar will contain 120 pieces of candy. Using the larger candies a jar will contain 80 pieces of candy. The candy maker has a strict rule that no jars will contain a mix of small and large candies. If a store has room for 15 jars and they want 1560 total pieces of candy, how many jars will contain smaller candies?

Answer 1

By creating a system of equations and solving for the variables, we find that 9 jars will contain smaller candies to achieve a total of 1560 pieces with 15 jars.

Step-by-step explanation:

To solve this problem, we can use a system of equations to represent the total number of candies and the total number of jars. Let x be the number of jars containing smaller candies, and let y be the number of jars containing larger candies. The two equations representing the conditions are:

1. Number of candies: 120x + 80y = 1560
2. Number of jars: x + y = 15

First, let's solve for y in the second equation:

y = 15 - x

Next, substitute y in the first equation and solve for x:

120x + 80(15 - x) = 1560

120x + 1200 - 80x = 1560

40x + 1200 = 1560

40x = 360

x = 9

So, 9 jars will contain smaller candies.

Answer 2

A.T.Q, your equation would be:

x+y=15 (x=jar of small candy;y=of larger candy)----1

120x+80y=1560---------------------------------------------2

Sunstitute value of y from equation 1, which is y=15-x

120x+80(15-x)=1560

120x-80x+1200=1560

40x=360

x=9

So, 9 jars will contain small candies.