Sam had foreign stamps and local stamps. After giving 1/4 of his foreign stamps and 11 local stamps, he had an equal number of foreign and local stamps. How many local stamps did he have in the beginning?
I got 32 for the answer by guessing and checking but what equation would I use to get that answer?
If he started with f foreign and g local stamps, then we have
3f/4 = g-11
3f = 4g-44
4g-3f = 44
so, if g=32, f = 28
But there are lots of other possibilities.
To solve this problem using an equation, let's consider the number of foreign stamps and local stamps that Sam had in the beginning.
Let's assume Sam had F foreign stamps and L local stamps initially.
According to the given information, after giving away 1/4 of his foreign stamps and 11 local stamps, Sam had an equal number of foreign and local stamps.
After giving 1/4 of his foreign stamps, Sam had (3/4)F foreign stamps remaining.
After giving 11 local stamps, Sam had (L - 11) local stamps remaining.
Since the number of foreign stamps remaining equals the number of local stamps remaining, we can set up an equation:
(3/4)F = L - 11
Now, let's solve the equation to find the value of L, which represents the initial number of local stamps:
Multiply both sides of the equation by 4:
4 * (3/4)F = 4 * (L - 11)
3F = 4L - 44
Rearrange the equation:
4L - 3F = 44
Now, let's select a value for F to find the corresponding value for L.
Based on your guess and check method, let's assume F = 36:
4L - 3(36) = 44
4L - 108 = 44
4L = 44 + 108
4L = 152
L = 152 / 4
L = 38
Therefore, in the beginning, Sam had 38 local stamps.