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?

1 answer

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.