Salina had some local and foreign stamps. The ratio of the number of local stamps to the number of foreign stamps was 3:4. She bought 21 more local stamps and the ratio became 9:8.
a. How many foreign stamps did Salina have?
b. How many local stamps did Salina have in the end?
To solve this problem, we can use a system of equations. Let's assign variables to the number of local and foreign stamps.
Let's say the number of local stamps Salina initially had is represented by "3x" (where x is a whole number), and the number of foreign stamps is represented by "4x".
According to the problem, the ratio of the number of local stamps to foreign stamps was initially 3:4. This can be written as:
(3x)/(4x) = 3/4
To simplify this equation, we can cross multiply:
3 * 4x = 4 * 3x
12x = 12x
This equation doesn't yield any information, so we need to look at the second piece of information given.
The problem states that Salina bought 21 more local stamps and the ratio became 9:8. This can be written as:
(3x + 21)/(4x) = 9/8
Again, cross multiplying:
8 * (3x + 21) = 9 * 4x
24x + 168 = 36x
Collecting like terms:
12x = 168
Now, we can solve for x by dividing both sides of the equation by 12:
x = 168/12
x = 14
Now that we know x, we can substitute it back into our equations to find the number of local and foreign stamps.
a. How many foreign stamps did Salina have?
The number of foreign stamps is represented by 4x:
4 * 14 = 56
Therefore, Salina had 56 foreign stamps.
b. How many local stamps did Salina have in the end?
The number of local stamps after Salina bought 21 more is represented by 3x + 21:
3 * 14 + 21 = 63
Therefore, Salina had 63 local stamps in the end.
using d for domestic and f for foreign,
d/f = 3/4
(d+21)/f = 9/8
42 local stamps
56 foreign stamps
check: 42/56 = 3/4
63/56 = 9/8