Erasers cost $5 per carton and pencils cost $7 per carton. If an order comes in for a total of 15 cartons for $85, how many cartons of each were bought?
5x+7y=85
substitute y for x: 5(15-y)+7y=85
75-5y+7y=85
75+2y=85
2y=10
y=5
So 5 pencils @ $7=$35 plus10 erasers @ $5, or $50, total $85.
Let's assume the number of cartons of erasers is x and the number of cartons of pencils is y.
The cost of x cartons of erasers is 5x dollars.
The cost of y cartons of pencils is 7y dollars.
According to the given information, the total cost is $85 and the total number of cartons is 15. So we can set up the following equations:
5x + 7y = 85 ..........(Equation 1)
x + y = 15 .............(Equation 2)
To solve this system of equations, we can use substitution or elimination method.
Let's solve it using the elimination method:
Multiply Equation 2 by 5 to make the coefficients of x in both equations equal:
5(x + y) = 5(15)
5x + 5y = 75 .........(Equation 3)
Now, subtract Equation 3 from Equation 1:
(5x + 7y) - (5x + 5y) = 85 - 75
2y = 10
y = 10/2
y = 5
Substitute the value of y in Equation 2 to find the value of x:
x + 5 = 15
x = 15 - 5
x = 10
Therefore, 10 cartons of erasers and 5 cartons of pencils were bought.
To solve this problem, we can set up a system of equations. Let's use the variables 'e' to represent the number of cartons of erasers and 'p' to represent the number of cartons of pencils.
Given that erasers cost $5 per carton and pencils cost $7 per carton, we can write the following equations:
1. The cost of erasers (5*e) plus the cost of pencils (7*p) equals the total cost of the order (85).
5e + 7p = 85
2. The total number of cartons ordered is 15.
e + p = 15
Now, we have a system of two equations. To solve it, we can use the method of substitution or elimination.
Let's use the method of substitution. Solving equation (2) for e, we get:
e = 15 - p
Now, we substitute this value for e in equation (1), and solve for p:
5(15 - p) + 7p = 85
75 - 5p + 7p = 85
2p = 10
p = 5
Now that we have the value of p, we can substitute it back into equation (2):
e + 5 = 15
e = 10
Therefore, 10 cartons of erasers and 5 cartons of pencils were bought.
Easier way:
$5*3=$15
$7*10=$70
70+15=$85
3 cartons of erasers were bought,and 10 cartons of pencils were bought