Percentage Question

Question

A cafe owner had some forks, knives and spoons. He had 327 knives and spoons. He had 348 knives and forks. After losing 10% of the forks and 3 spoons, he had an equal number of forks and spoons. What percentage of the remaining number of forks, knives and spoons he had was the number of knives?

Answer 1

k=# of knives

s=# of spoons

f=# of forks

327=k+s

348=k+f

 

he lost 10% of the forks so he has 90% of the forks left; 90%f=0.9f

he lost 3 spoons so he has s-3 spoons left

the number of forks and spoons are the same

0.9f=s-3

s=0.9f+3

substitute into 327=k+s

327=k+(0.9f+3)

348=k+f

327-3=k+0.9f

324=k+0.9f

use this equation and 348=k+f

348=k+f

324=k+0.9f

subtract equations

24=0.1f

240=f

there are 240 forks

348=k+240

348-240=k

k=108 knives

327=k+s

327=108+s

327-108=s

s=219 spoons

he has 90% of forks left; 0.9*240=216 forks left

he lost 3 spoons, so 219-3=216 spoons left which is correct because he has an equal number of forks and spoons

he has 216 spoons, 216 forks, and 108 knives remaining

216+216+108=540 pieces of cutlery left

108/540=??

you can divide or simplify the fraction

108/540=54/270=6/30=1/5=2/10=20/100=20% of the remaining cutlery are knives (or just divide:108/540=0.2=20%)

Answer 2

Good morning,

 

k + s = 327

 

k + f = 348

 

.9f =s-3

 

solve for f

 

f = (s/.9) - (3/.9)

 

f = 10s/9 - 30/9

 

plug this expression in for f in the equation k + f = 348

 

k + 10s/9 - 30/9 = 348

 

subtract the equation k + s = 327

 

s/9 - 30/9 = 21

 

multiply by 9

 

s - 30 = 189

 

s = 219

 

plug into k + s =327

 

k = 108

 

plug into k + f = 348

 

f = 240

 

He originally had 108 knives, 240 forks, 219 spoons but he lost 10% of the forks and 3 spoons,

 

He now has 108 knives, 216  forks and 216 spoons for a total of 540 utensils

 

the number of knives as a percent of the total = 108/540

 

= 20%