two word problems i am having trouble with

Question

1. Jack can do a certain job in 20 mins less time than Allen can do the same job. One day Jack starts the job but stops after 10 minutes due to getting hurt. Allen steps in and finishes the job after working for 15 minutes. How long can Jack do this job by himself if he were not injured? Answer must be rounded to nearest tenth.

1. A retailer bought a number of collectible cups for $48. She keeps two of the cups for herself and sells the remaining cups for $3 more thanthe original cost per cup. If she sells the remaining cups for $70, how many cups did she buy and at what price per cup did she sell? Let x be the number of cups she purchased.

Answer 1

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

Answer 2

t represents Allen's time working alone

t - 20 represents Jack's time working alone

10 / (t - 20) + 15 / t = 1

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

Can you solve for t and answer?

x represents number of cups purchased

x - 3 represents number of cups sold

48/x represents price per cup purchased

48/x + 3 represents price per cup sold

(48/x + 3)(x - 3) = 70

Can you solve so x and answer?