Answer:
Step-by-step explanation:
Let's create some equations first.
Say M = number of months, T = Todd and S = Sally.
We know that Todd starts with 8 cds and sally starts with 18 cds.
This means when M= 0, T = 8 and S = 18
After one month (M = 1), Todd adds 9 cds.
This means can write the following equation:
T = 8 + 9M
So after the first month (where M = 1), we can find out that Todd has
T = 8 + 9 x 1 = 8 + 9 = 17 cds
For Sally, we know she adds 7 cds per month.
S = 18 + 7M
After one month (M = 1),
S = 18 + 7 x 1 = 25 cds.
Now we are trying to find when they will have the same number of cds and how many.
This means we are trying to figure out what M = ? when Todd and Sally are equal.
So we want to find when T = S
Remember, earlier we wrote :
T = 8 + 9M
S = 18 + 7M
If T = S, this means:
8 + 9M = 18 + 7M
Gather the like terms and solve for M.
Subtract 8 from both sides.
9M = 10 + 7M
Subtract 7M from both sides
2M = 10
Divide both sides by 2
M = 5.
So in 5 months, we are saying T = S (Todd and Sally will have the same number of cds).
Put M = 5 back into our earlier equations to find out how many cds they have after 5 months.
T = 8 + 9M
T = 8 + 9 x 5
T = 53
Therefore, after 5 months Todd and Sally will have 53 cds each :)
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