A stamp collection consists of 3¢, 12¢, and 15¢ stamps. The number of 3¢ stamps is three times the number of 12¢ stamps. The number of 15¢ stamps is three less than the number of 12¢ stamps. The total value of the stamps in the collection is $2.43. Find the number of 15¢ stamps in the collection.
Please, Im really struggling with these types of problems.
If someone could just show me how to set up a formula that would be great!
3 cent = x
12 = y
15 = z
x = 3 y
z +3 = y
3 x + 12 y + 15 z = 243
3 (3y) + 12 y + 15 (y-3) = 243
get it ?
so it would then turn into 9y+12y+15y-45=243
36y-45=243 ( add the y's together)
36y = 288 (add 45 to 243)
y = 8? (288 divided by 36)
yes, y is 8 but it asked for z
z = y-3 = 5
OHH! Thank you very much, that would have been a pretty frustrating error if I continued without noticing! Thank you, Damon. Have a great night!
You are welcome.
To solve this problem, we need to set up a system of equations based on the given information and then solve for the unknown variables.
Let's define the variables:
Let x be the number of 3¢ stamps.
Let y be the number of 12¢ stamps.
Let z be the number of 15¢ stamps.
Based on the given information, we can write the following equations:
1) The number of 3¢ stamps is three times the number of 12¢ stamps: x = 3y.
2) The number of 15¢ stamps is three less than the number of 12¢ stamps: z = y - 3.
3) The total value of the stamps in the collection is $2.43: 3x + 12y + 15z = 243¢.
Now let's solve this system of equations:
Substitute equation (1) into equation (3):
3(3y) + 12y + 15z = 243
9y + 12y + 15z = 243
21y + 15z = 243
Divide both sides of the equation by 3 to simplify:
7y + 5z = 81 ---- (4)
Substitute equation (2) into equation (4):
7y + 5(y - 3) = 81
7y + 5y - 15 = 81
12y = 96
Divide both sides of the equation by 12 to solve for y:
y = 8
Now substitute the value of y back into equation (2) to solve for z:
z = y - 3
z = 8 - 3
z = 5
Therefore, the number of 15¢ stamps in the collection is 5.