Percentage Problems

[phoenix9801]

I need some clarification of the 2 problems please. If you can explain step-by-step instruction I would greatly appreciate it. Be Simple...


1- At a certain pizzeria, 1/8 of the pizzas sold one week were mushroom and 1/3 of the remaining pizzas sold were pepperoni. If n of the pizza sold were pepperoni, how many were mushroom?



2- A $500 investment and a $1,500 investment have a combined yearly return of 8.5 percent of the total of the two investments. If the $500 investment has a yearly return of 7 percent, what percent yearly return does the $1,500 investment have?

[kvcpk]

problem1:

let number of pizzas sold be x

x/8 = mushrooms
remaining=7x/8
1/3 of remaining = pepper
1/3(7x/8) = pepper = n

7x/24=n
x=24n/7
so mushroom = x/8 = 3n/7

[selango]

8.5/100*2000=7/100*500+x/100*1500

Solving we get x=9

1500 investment with yearly return of 9%

[amising6]

1)let no of pizzas be x
mushroom pizza sold = 1/8 of x=x/8
remaining pizza=x-x/8=7x/8
pepperoni sold 1/3 of the remaining=1/3 of 7x/8=7x/24
now according to problem 7x/24=n i.e x=24n/7
no of pizza which were mushroom x/8
=(24n/7)/8 (substituating x=24n/7)
=3n/7


2)A $500 investment and a $1,500 investment have a combined yearly return of 8.5 percent of the total of the two investments
total investment 500+1500=$2000
total yearly return 8.5%of 2000=170

now if we take $500 individually
%return is 7%
return from $500 investment 7%of500=$35

so return from 1500 =total return- return from $500
=170-35
=135
return % =(135/1500)*100=9% answer

[phoenix9801]

1)let no of pizzas be x
mushroom pizza sold = 1/8 of x=x/8
remaining pizza=x-x/8=7x/8
pepperoni sold 1/3 of the remaining=1/3 of 7x/8=7x/24
now according to problem 7x/24=n i.e x=24n/7
no of pizza which were mushroom x/8
=(24n/7)/8 (substituating x=24n/7)
=3n/7


2)A $500 investment and a $1,500 investment have a combined yearly return of 8.5 percent of the total of the two investments
total investment 500+1500=$2000
total yearly return 8.5%of 2000=170

now if we take $500 individually
%return is 7%
return from $500 investment 7%of500=$35

so return from 1500 =total return- return from $500
=170-35
=135
return % =(135/1500)*100=9% answer

In Problem # 1

How did you move from 7x / 24 = n to x =24n/7 and why did you do it that way ???
can you please explain step-by-step instructions

[selango]

phoenix9801,

Number of Pepperoni pizzas is 7x/24,where x is total number of pizzas.

Now according to the question,n of the pizza sold were pepperoni(ie) number of pepperoni pizzas sold is equal to n.

So 7x/24=n


Hope this clarify

[amising6]

How did you move from 7x / 24 = n to x =24n/7 and why did you do it that way ???
can you please explain step-by-step instructions
thats cross multiplication

7x/24=n
then we can write 7x=24n
so x can be 24n/7
hope this clears