At its grand opening, the gutherie market distributed two different types of souvenirs. One type costs 20 centseach, and the other type costs 25 cents each. One thousand souvenirs were distributed in all. If the cost of these souvenirs was $220, how many of each type were distributed?
Let x = One souvenir
Let (1000 - x) = Other souvenir
Equation:
.25(x) + .20(1000 - x) = 220
Solve for x. Remember to include both souvenir types in your answer.
GTA V came out no one wants to answer
To solve this problem, we can use a system of equations. Let's denote the number of souvenirs of the first type as 'x' and the number of souvenirs of the second type as 'y'. We have the following information:
1. The cost of the first type of souvenir is 20 cents each, and the cost of the second type is 25 cents each.
2. A total of 1000 souvenirs were distributed.
3. The cost of all the souvenirs combined is $220.
From the first piece of information, we can set up the equation: x souvenirs * 20 cents = $0.20x. Similarly, for the second type, we have y souvenirs * 25 cents = $0.25y.
Next, we can use the second and third pieces of information to form another equation. The total number of souvenirs is the sum of x and y: x + y = 1000. The total cost of all the souvenirs is $220: $0.20x + $0.25y = $220.
Now, we have a system of equations:
$0.20x + $0.25y = $220 ---(1)
x + y = 1000 ---(2)
To solve this system, we can use various methods like substitution or elimination. Let's use substitution:
From equation (2), we have x = 1000 - y.
Substituting this value in equation (1):
$0.20(1000 - y) + $0.25y = $220
$200 - $0.20y + $0.25y = $220
$0.05y = $20
y = $20 / $0.05
y = 400
Now, substitute the value of y back into equation (2):
x + 400 = 1000
x = 1000 - 400
x = 600
Therefore, 600 souvenirs of the first type and 400 souvenirs of the second type were distributed.