Arthur D. answered • 10/16/19

Effective Mathematics Tutor

1.) Allen takes x minutes to do the job

Jack takes x-20 minutes to do the job

1/(x-20)(10)+(1/x)(15)=1 (job done)

multiply both sides by x(x-20) to get...

10x+15(x-20)=x(x-20)

10x+15x-300=x^2-20x

x^2-20x-25x+300=0

x^2-45x+300=0

use the quadratic equation

{45±√(2025-1200)}/2

{45±√825}/2

(45±28.7228)/2

73.7228/2

36.86 minutes

36.7 minutes for Allen

36.86-20=16.7 minutes for Jack

check: (1/16.7)(10)+(1/36.7)(15)=1

0.5988+0.4087=1.0075 (this exceeds 1 because you rounded up)

2.) x=# of cups

y=cost of one cup

xy=$48

(x-2)(y+3)=70

xy=48 implies x=48/y

substitute

([48/y]-2)(y+3)=70

multiply both sides by y to get...

(48-2y)(y+3)=70y

48y-2y^2+144-6y=70y

combine similar terms and get all terms on one side

2y^2+28y-144=0

y^2+14y-72=0

factor or use the quadratic equation

(y+18)(y-4)=0

y=-18 makes no sense

y=4

$4 per cup for the cost and 12 cups were bought (48/4)

check: keep 2 cups and sell 10 cups for $3 more than $4 or sell for $7 each

10*$7=$70