Answer:
1 pen costs $0.75, and 1 pencil costs $0.25.
Explanation:
Let x = price of 1 pen.
Let y = price of 1 pencil.
John:
20x + 50y = 27.5
Jessica:
10x + 40y = 17.5
System of equations:
20x + 50y = 27.5
10x + 40y = 17.5
Rewrite the first equation. Multiply both sides of the second equation by -2 and write it under the first equation. Add the equations.
20x + 50y = 27.5
+ -20x - 80y = -35
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-30y = -7.5
Divide both sides by -30.
y = -7.5/(-30)
y = 0.25
Use the first equation.
20x + 50y = 27.5
Substitute 0.25 for y and solve for x.
20x + 50(0.25) = 27.5
20x + 12.5 = 27.5
Subtract 12.5 from both sides.
20x = 15
Divide both sides by 20.
x = 15/20
x = 0.75
Answer: 1 pen costs $0.75, and 1 pencil costs $0.25.