it's a system of equations
5 V + 3 C + 2 M = 675
V = 2 C
M = C + 75
substitute and solve
Vanilla cookies $5/ box
Chocolate cookies $3/box
Mint cookies $2/box
Mary was selling girl guide cookies. She sold twice as many vanilla cookies as she did chocolate cookies. She sold 75 more boxes of mint cookies as she did chocolate cookies. The total sale of the cookies is $675. How many boxes of each type of cookie did she sell?
5 V + 3 C + 2 M = 675
V = 2 C
M = C + 75
substitute and solve
- Let V represent the number of boxes of vanilla cookies sold.
- Let C represent the number of boxes of chocolate cookies sold.
- Let M represent the number of boxes of mint cookies sold.
Now let's translate the given information into equations.
1. "Mary sold twice as many vanilla cookies as she did chocolate cookies."
This statement tells us that the number of vanilla cookies sold (V) is twice the number of chocolate cookies sold (C). So we can write the equation as:
V = 2C
2. "Mary sold 75 more boxes of mint cookies than she did chocolate cookies."
This statement tells us that the number of mint cookies sold (M) is 75 more than the number of chocolate cookies sold (C). So we can write the equation as:
M = C + 75
3. The total sale of the cookies is $675.
This statement tells us that the total cost of the vanilla cookies (5V), chocolate cookies (3C), and mint cookies (2M) is equal to $675. So we can write the equation as:
5V + 3C + 2M = 675
Now we have three equations:
V = 2C
M = C + 75
5V + 3C + 2M = 675
With these equations, we can solve for the values of V, C, and M to find how many boxes of each type of cookie Mary sold.