Sam had a total of 80 foreign stamps and local stamps combined. After giving away 1/3 of his foreign stamps and 10 local stamps, he had an equal number of foreign stamps and local stamps left. How many local stamps did he have in the beginning?
f+l = 80
2/3 f = l-10
so,
2/3(80-l) = l - 10
160-2l = 3l-30
190 = 5l
l = 38
check:
initially there were
38 local and 42 foreign
after removing 10 local and 14 foreign, there were 28 of each.
The 2/3rds come from how much is left after 2/3rds are gone.
Where do you get 2/3rds from
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To solve this problem, let's break it down step by step:
Step 1: Let's assume that Sam had "x" local stamps in the beginning.
Step 2: We know that Sam had a total of 80 foreign stamps and local stamps combined. So, we can write the equation: x + (80 - x) = 80, where (80 - x) represents the number of foreign stamps Sam had.
Step 3: According to the problem, Sam gave away 1/3 of his foreign stamps. So, the number of foreign stamps left would be (80 - x) - (1/3)(80 - x).
Step 4: After giving away 10 local stamps, Sam had an equal number of foreign stamps and local stamps left. Therefore, we can set up the equation: x - 10 = (80 - x) - (1/3)(80 - x).
Step 5: Simplifying the equation, we have: x - 10 = (80 - x) - (80 - x)/3.
Step 6: Solving for x, we find: x - 10 = (2/3)(80 - x).
Step 7: Expanding the equation, we get: 3x - 30 = 160 - 2x.
Step 8: Combining like terms, we obtain: 5x - 30 = 160.
Step 9: Moving the constant to the other side of the equation, we have: 5x = 160 + 30.
Step 10: Adding the values, we get: 5x = 190.
Step 11: Dividing both sides by 5, we find: x = 38.
Therefore, Sam had 38 local stamps in the beginning.