I just need help setting up the equations . I dont know if they are asking to find cans or weeks.
Students in the Healthy Planet Club at Eagle High School are collecting aluminum cans as part of a community cleanup project. Together, the 9th graders and 10th graders hope to collect 10,000 cans. Before the contest begins the 9th graders class advisor gave his students 200 cans that he saved in his garage. The 10th grade class advisor gave her class 850 cans and her family and neighbors had collected. The 9th graders brought in 400 cans per week and the tankers collected 350 each
Represent each class with an equation to find any variables used in the equation when will the 9th and 10th graders have the same number of cans? How many cans will they have? How many weeks before 10,000 cans are collected by the two groups working together?
after w weeks, the amounts are:
9th grade = 200+400w
10th grade = 850+350w
now you should be able to answer the questions.
Thank you steve thats what i had but wasnt sure
To set up the equations, let's assign variables to the unknowns.
Let's say:
x = the number of weeks it takes for the 9th graders and 10th graders to have the same number of cans
n = the number of cans the 9th graders have in total
t = the number of cans the 10th graders have in total
We know that the total number of cans the 9th and 10th graders hope to collect is 10,000. So we can set up the equation:
n + t = 10,000 ---(Equation 1)
Before the contest begins, the 9th-grade class advisor gave his students 200 cans, so initially, the 9th graders have n + 200 cans. And the 10th-grade class advisor gave her class 850 cans, so initially, the 10th graders have t + 850 cans. We can express these in equations:
n + 200 = x * 400 ---(Equation 2)
t + 850 = x * 350 ---(Equation 3)
To find when the 9th and 10th graders will have the same number of cans, we can set Equations 2 and 3 equal to each other:
n + 200 = t + 850
n - t = 850 - 200
n - t = 650 ---(Equation 4)
Now we have three equations: Equation 1, Equation 4, and Equation 3. We can solve these equations simultaneously to find the values of n, t, and x.
To find when they will have the same number of cans, we need to solve Equation 4. We can rearrange Equation 4 to express t in terms of n:
t = n - 650
Now, substitute the value of t back into Equation 1:
n + (n - 650) = 10,000
2n - 650 = 10,000
2n = 10,000 + 650
2n = 10,650
n = 10,650 / 2
n = 5,325
Therefore, the 9th graders will have 5,325 cans when the 10th graders also have 5,325 cans.
To find out how many weeks it takes to collect 10,000 cans by the two groups working together, substitute the value of n back into Equation 2:
5,325 + 200 = x * 400
5,525 = 400x
x = 5,525 / 400
x ≈ 13.81
Therefore, it will take approximately 14 weeks for the 9th and 10th graders working together to collect 10,000 cans.
In summary:
- The 9th and 10th graders will have the same number of cans (5,325 cans) when the number of weeks (x) is approximately 14 weeks.
- It will take approximately 14 weeks for the two groups to collect a total of 10,000 cans.