Algerbra problem confusion, please help??

Question

Giordano's Pizza Shop is famous for its spectacular Giordano's Giant, a large gourmet pizza that's big enough to feed 16 people! There is a base charge for the plain pizza, and then an additional charge per topping ordered from the list of 20 possible items. All the toppings are priced equally.


A Giordano's Giant pizza ordered with 2/5 of the possible toppings will cost $46.50. One with 30% of the possible toppings will cost $41.80. Using that information, answer the following questions:

Find an equation that expresses the total cost of a Giordano's Giant pizza in terms of the number of toppings ordered.

How much would a Giant pizza with all the possible toppings cost?

If a customer ordered a Giant pizza that cost $55.90, what percent of the toppings did she order?


i'm only an 8th grader , please help.

Answer 1

2/5 of 20 possible toppings is 8 toppings.
30% of 20 possible toppings is 6 toppings.

The difference between the two pizza prices is 46.50-41.80, or $4.70. This is the difference between a pizza with 8 toppings vs. 6, or the price difference for two toppings.

So, each topping costs half of that, or $2.35.

Take one of the pizza prices, and subtract the extra topping prices to get the price of a plain pizza. $41.80 - 6(2.35)
= $27.70

The total cost of a pizza is plain_price + number_of_toppings * topping_price, or total = $27.70 + n($2.35) (where n is the number-of-toppings)

A pizza with all of the toppings would cost $27.70 + 20($2.35) = $74.70

For the $55.90 pizza, take the $55.90 and subtract the price of a plain pizza, to see how much the $55.90 pizza's toppings cost:
55.90-27.70 = $28.20 in toppings. (Wow that's expensive!)

Divide the toppings price by the price-per-topping to find out how many there were: 28.20/2.35 = 12.

12 toppings out of 20 means 12 / 20 = 0.6, or 60%

Answer 2

Ok set the base charge as x. Let the number of total toppings be n. Price per topping is p.
2/5=0.4
30%=0.3
So x+0.4np=46.50
And x+0.3np=41.80
Using the second equation, if you add 4.70 to both sides, you get: x+0.3np+4.70=46.50
Because of that, you can plug in x+0.3np+4.70 as the 46.50 of the first equation, so:
x+0.3np+4.70=x+0.4np, and you solve that for np
4.70=0.1np
np=47
Because n is the number of total toppings, and p is the price per topping, the price of all the toppings together is $47.
So then for the base cost, you plug in 47 as np of either of the given equations. I'll use the first one.
x+0.4np=46.50
x+0.4(47)=46.50
x+18.80=46.50
x=27.7, so the base cost is $27.70. For a pizza with all the the toppings, you just add $47 to the base cost, so $27.70+$47=$74.70 is the cost of a giant pizza with all the possible toppings.

For the second question, it's a lot easier because you already have all of the values. Let's put the percent of toppings as t.
x+tnp=55.90, because we know x is 27.70 and np is 47, we plug them in.
27.70+47t=55.90
47t=28.2
t=0.6
So the percent of toppings in decimal form is 0.6, or 60%. Therefore, the percent of toppings the person in the second problem ordered is 60%.

Answer 3

let's call Plain Pizza : PP
let x be the number of toppings.

46.50 = PP + (2/5)(20)(x) = PP + 8x
and
41.80 = PP + (30/100)(20)(x) =PP+6x

we have 2 equations to solve for 2 unknowns (PP and x)
PP +8x = 46.50 <--- eq1
PP +6x = 41.80 <---- eq2
Substract eq2 from eq1 to get
8x -6x = 46.50 - 41.80
2x = 4.70
the cost of a topping x = $2.35
Let's use eq1 to find PP
PP +8(2.35) =46.50
PP + 18.80 = 46.50
PP = 46.50 -18.80 = $27.70
The equation for the cost of any pizza with any toppings(from 0 to 20)is
C = $27.70 + $2.35x.

How much would a Giant pizza with all the possible toppings cost?
C = $27.70 +$2.35(20) =$74.70

If a customer ordered a Giant pizza that cost $55.90, what percent of the toppings did she order?

$55.90 = $27.70 + $2.35x
Find x
2.35x = 55.90 -27.70 =28.2
x = 28.2/2.35 =12 toppings
The % of toppings she ordered was
(12/20 )*100% = 60%

Answer 4

2/5 of possible toppings = 2/5 * 20 = 8 toppings
30% of possible toppings = .3 * 20 = 6 toppings
b = base cost
x = xtra cost per topping
b + 8x = 46.50
b + 6x = 41.80
2x = 4.70
x = 2.35
b = 27.70
Cost = $27.70 + $2.35x (that's the equation)

C for pizza with 20 items = 27.7 + 2.35*20 = $74.70

$55.90 = $27.70 + $2.35x
$28.20 = $2.35x
12 = x (number of toppings)
12/20 = 60% (percent of the toppings)

Expensive pizza!

Answer 5

for question number one the equation should be:
27.7 + 2.35w= total price of pizza with (w) number of toppings

for number two:
27.7 + 2.35(20)= 74.7= total price of pizza with all toppings

for number three:
27.7 + 2.35w = 55.90
2.35w= 28.2
w= 12 toppings
12/20 = x/100
x= 60
therefore, the customer ordered 60% of the toppings

HI I'm JAMIE and I'm an 11 yr. old sixth grader from stockton :)