Answer:
a pen costs $5, and pencil costs $3.
Explanation:
This can be solved using simultaneous equations:
let cost of pens be x
let cost of pencils be y
∴ 7x + 5y = 50 (1)
5x + 7y = 46 (2)
We have two equations, and we can solve them by first subtracting equation (1) from equation (2), and eliminating a variable. But in this case, we should first multiply (1) by 7, and (2) by 5. Doing this, will ensure one of the terms is common in both equations and can be eliminated.
49x + 35y = 350 (3)
25x + 35y = 230 (4)
Now subtracting (4) from (3), we get: 24x + 0 = 120
∴24x = 120
x = 5
Now we have the value of x, we can substitute this into one of the original equations, say, (1), and solve the resulting equation, to find the value of y.
∴ 7(5) + 5y = 50
35 + 5y = 50
5y = 15
y = 3
Therefore, a pen costs $5, and pencil costs $3.