The base equation is: 8x + 6y = 8.50. (x is pencils and y is pens)
We also know that 4x + 4y = 5.00. Let's solve this equation for y.
4x+4y = 5.00
4y = 5.00 - 4x
y = 5.00 - 4x /4
Plug this into the base equation.....
8x + 6 x 5-4x /4 = 8.50
8x + 3x 5-4x /2 = 8.50 (Reduce the fraction by dividing the numerator and denominator by 2)
8x + 3x5-3x4x /2 = 8.50 (multiply the values)
8x = 15-12x /2 = 8.50
2x8x + 2 x 15-12x /2 = 2x8.50 (multiply both equation sides by 2)
2x8x+15-12x=2x8.50 (reduce the fraction by dividing the numerator and denominator by 2)
16x + 15 - 12x = 2x8.50
4x + 15 = 2 x 8.50 (Calculate the difference)
4x + 15 = 2 x 85/10 (write the value as a fraction)
4x + 15 = 2x17/2 (reduce the fraction by diving the N and D by 5)
4x + 15 = 17 (reduce the fraction by diving the N and D by 2)
4x = 17 - 15 (rearrange the values)
4x = 2 (calculate the difference)
x= 2/4 (divide both equation sides by 4)
x = 2/4 (write as a fraction)
x= 1/2 (reduce the fraction by dividing the N and D by 2)
x = 0.5 (alternate decimal form) = in simple terms of cost is 50 cents
Plug that into either one of the equations to get y, which is .75 or 75 cents
8(.50) + 6y = 8.50
4.00 + 6y = 8.50
6y = 4.50
y = .75
OR
4(.50) + 4y = 5.00
2.00 + 4y = 5.00
4y = 3.00
y = .75
I'll take a chocolate bar as compensation, please. And you're welcome. :-)
