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? a. pen, $0.75; pencil, $0.50 b. pen, $0.50; pencil, $0.25 c. pen, $1.00; pencil, $0.25 d. pen, $0.80; pencil, $0.35 e. pen, $1.20; pencil, $0.25

A. pen, $0.75; pencil, $0.50

Step-by-step explanation:

let pen be $x n pencil be $y

8 pencils and 6 pens cost a total of $8.50

(1) 8y + 6x = 8.5

4 of each cost $5

(2) 4y + 4x = 5

multiply (2) by 2:  8y + 8x = 10

subtract (1) from (2)x2:  8x - 6x = 10 - 8.5

2x = 1.5

x = 0.75

put back in (1):  8y + 6*0.75 = 8.5

8y = 8.5 - 4.5 = 4

y = 0.5

ans is A. pen, $0.75; pencil, $0.50

more detail

step-by-step explanation:

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.