Terry bought some gum and candy. The number of packages of chewing gum was one more than the number of mints. The number of mints was three times the number of candy bars. If gum was 6 cents a package, mints were 3 cents each, and candy bars were 10 cents each, how many of each did he get for 80 cents?
Isolate and then Substitute
Well, it's already isolated for you anyway, so it should be even easier.
To solve this problem, we need to set up equations based on the given information.
Let's represent the number of packages of chewing gum as G, the number of mints as M, and the number of candy bars as C.
Based on the information given:
1. The number of packages of chewing gum (G) was one more than the number of mints (M).
Equation 1: G = M + 1
2. The number of mints (M) was three times the number of candy bars (C).
Equation 2: M = 3C
Next, let's calculate the cost of each item and set up an equation for the total cost.
The cost of gum (G) is 6 cents per package, so the cost of G packages will be 6G cents.
The cost of mints (M) is 3 cents each, so the cost of M mints will be 3M cents.
The cost of candy bars (C) is 10 cents each, so the cost of C candy bars will be 10C cents.
The total cost of Terry's purchase is 80 cents.
Equation 3: 6G + 3M + 10C = 80
Now, we have a system of three equations:
1. G = M + 1
2. M = 3C
3. 6G + 3M + 10C = 80
We can solve this system of equations to find the values of G, M, and C that satisfy all three equations and correspond to a total cost of 80 cents.
what have they told you?
g = m+1
m = 3c
6g+3m+10c = 80
Now crank it out