Two coworkers picked up some writing instruments at the office supply store. Andy selected 7 boxes of pencils and 5 boxes of ballpoint pens, paying $34. Next, Eliana spent $48 on 8 boxes of pencils and 8 boxes of ballpoint pens. How much does a box of each cost?
Two coworkers picked up some writing instruments at the office supply store. Julian selected 1 box of pencils and 1 box of ballpoint pens, paying $6. Next, Aubrey spent $16 on 1 box of pencils and 3 boxes of ballpoint pens. How much does a box of each cost?
2 and 4
To find the cost of a box of pencils and a box of ballpoint pens, we can set up a system of equations based on the information provided.
Let's assume the cost of a box of pencils is x dollars and the cost of a box of ballpoint pens is y dollars.
From the given information, we can form two equations:
Equation 1: 7x + 5y = 34 (Andy's purchase)
Equation 2: 8x + 8y = 48 (Eliana's purchase)
We now have a system of equations. To solve this system, we can use the method of substitution or elimination.
Let's use the method of substitution:
From Equation 1, express x in terms of y:
x = (34 - 5y) / 7
Substitute this value of x in Equation 2:
8((34 - 5y) / 7) + 8y = 48
Now we can solve for y:
(8(34 - 5y) / 7) + 8y = 48
Multiply through by 7 to eliminate the fraction:
8(34 - 5y) + 56y = 336
272 - 40y + 56y = 336
Combine like terms:
16y = 64
Divide both sides by 16:
y = 4
Now substitute this value of y back into Equation 1 to find x:
7x + 5(4) = 34
7x + 20 = 34
Subtract 20 from both sides:
7x = 14
Divide both sides by 7:
x = 2
Therefore, a box of pencils costs $2 and a box of ballpoint pens costs $4.
7p+5b = 34
8p+8b = 48
Now solve as usual