Erasers cost $5 per carton and pencils cost $7 per caron. If an order comes in for a total o 15 cartons for $85, how many cartons of each were brought?
Using system of equations:
E=number of cartons of erasers
P=number of cartons of pencils
5E+7P=85
E+P=15
Solve for E and P.
Easier: We know E+P=15, so directly write
5E+7(15-E)=85
Solve for E and then find P=15-E.
Even easier, do it mentally:
15 cartons of erasers cost 5*15=75.
Since total cost is $85, so the $10 left is to exchange erasers for pencils at $(7-5)=$2 per carton, which means there are 5 cartons of pencils, and 15-5=10 cartons of erasers.
To solve this problem, we need to set up a system of equations based on the given information.
Let's assume the number of cartons of erasers is represented by "E" and the number of cartons of pencils is represented by "P".
We know that erasers cost $5 per carton, so the cost of erasers can be expressed as 5E. Similarly, the cost of pencils can be expressed as 7P.
The total number of cartons is given as 15, so we can write the first equation as:
E + P = 15
The total cost of the order is $85, so we can write the second equation as:
5E + 7P = 85
Now, we have a system of equations:
E + P = 15
5E + 7P = 85
To solve this system, we can use the method of substitution or elimination.
Let's solve this system using the substitution method:
From the first equation, we have E = 15 - P.
Substitute this expression for E into the second equation:
5(15 - P) + 7P = 85
Simplify the equation:
75 - 5P + 7P = 85
2P = 10
P = 5
Now, substitute the value of P back into the first equation:
E + 5 = 15
E = 15 - 5
E = 10
Therefore, 10 cartons of erasers and 5 cartons of pencils were brought.