Question
Rodrick had a certain number of sweets. If he gives 3 sweets to each of his friends, he will have 7 sweets left. If he gives 5 sweets to each of his friends, he will need 9 more sweets. How many friends does he have?
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Let's call the number of sweets Rodrick has "x" and the number of friends he has "f".
From the first sentence, we know that:
x - 3f = 7
From the second sentence, we know that:
x - 5f = -9
Now we can solve for f by using either of these equations.
Let's use the first one:
x - 3f = 7
x = 3f + 7
Now we can substitute this expression for x in the second equation:
3f + 7 - 5f = -9
-2f = -16
f = 8
So Rodrick has 8 friends.
To check, we can substitute this value of f into one of the original equations:
x - 3f = 7
x - 3(8) = 7
x - 24 = 7
x = 31
So Rodrick has 31 sweets.
Now we can check the other equation as well:
x - 5f = -9
31 - 5(8) = -9
31 - 40 = -9
-9 = -9
Both equations check out, so we can be confident in our answer of 8 friends.
From the first sentence, we know that:
x - 3f = 7
From the second sentence, we know that:
x - 5f = -9
Now we can solve for f by using either of these equations.
Let's use the first one:
x - 3f = 7
x = 3f + 7
Now we can substitute this expression for x in the second equation:
3f + 7 - 5f = -9
-2f = -16
f = 8
So Rodrick has 8 friends.
To check, we can substitute this value of f into one of the original equations:
x - 3f = 7
x - 3(8) = 7
x - 24 = 7
x = 31
So Rodrick has 31 sweets.
Now we can check the other equation as well:
x - 5f = -9
31 - 5(8) = -9
31 - 40 = -9
-9 = -9
Both equations check out, so we can be confident in our answer of 8 friends.
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