Sam wants to buy 8 pencils and 6 pens, which cost a total of $8.50. he realizes he doesn't have enough cash and instead takes only 4 of each, which costs only $5. what is the price of each pen and pencil?

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.  :-)

ad = ae + ed = y + 7

similar triangles therefor

ac/ab = ad/ae

6/4 = (y + 7) / y

cross multiply

6y = 4(y + 7)

6y = 4y + 28

2y = 28

y = 14

step-by-step explanation: