Word algebra problem....I can't get it in my head?

Question

Annie ordered 38 pizzas for the class party. Small pizzas cost $9.00 and Large pizzas cost $12.50. If the total bill was $415.50, how many small pizzas did Annie order?
I cannot seem to get my head aroundthis. The more I look the more confused I get. Help please !!

Answer 1

Let

S = number of small pizzas
L = number of large pizzas

We have:

S + L = 38
S = 38 - L

9S + 12.50L = 415.50

Substituting

9(38 - L) + 12.50L = 415.50
342 - 9L + 12.50L = 415.50
3.50L = 73.50
L = 73.50/3.50 = 21
S = 38 - L = 38 - 21 = 17

Annie ordered 17 small pizzas.

Answer 2

When confused about a word problem, just start replacing words with symbols. It becomes a lot easier.

Annie ordered P=38 pizzas for the class party. Small pizzas (S) cost $9.00 and Large pizzas (L) cost $12.50. If the total bill (+) was C=$415.50, how many small pizzas did Annie order?

S: number of small pizzas (cost $9.00 each)
L: number of large pizzas (cost $12.50 each)
P: total number of pizzas
C: total cost

Obviously, there are only small and large pizzas so their sum is the total number of pizzas or:

S+L = P = 38

The cost works the same way. Multiply the cost of each pizza with how many were purchased.

S * $9.00 + L * $12.50 = C = $415.50

So you now have two equations and two variables. You just have to solve for S. I will leave that up to you.

S * $9.00 + L * $12.50 = $415.50
S+L = 38

Answer 3

Let's start from the beginning.
You have the following information. You have 38 pizzas, you know the price for each of the two different pizzas she bought and you know how much she paid for all.
Lets say S= number of small pizzas and L=number of Large Pizzas.
So we have
(S*9.00) + (L*12.50) = 415.50.
But here we have to unknown variables S and L and we cant resolve the problem. So now you use the other given information in the problem. 38 pizzas.
So you have
S + L = 38 . We can write the formula as it follows
S= 38 - L.
Now we can replace S for 38 - L and then we can solve the first formula.
Now you have
(38-L)*9.00 + L*12.50 = 415.50
You can resolve this formula, there is only one variable.
Now, L = 21
We know that S + L = 38 , we have that S = 17

so, 21 large pizzas and 17 small ones

Answer 4

Well you know you have 38 pizzas so. Let x represent the number of Small Pizzas and y represent Large pizzas. You would have the equation:
x+y=38

Solve for y and you get y= 38-x

This will lead us to the main equation in which we multiply the number of small pizzas by $9.00 and add that to the number of large pizzas multiplied by $12.50. This should equal $415.50. This gives us this equation:

(y*9)+12.5(38-y)=415.5

Now just solve for y and that is the number of small pizzas ordered.

Answer 5

x + y = 38- - - - - - - - - - -- - Equation 1
9x + 12.50y = 415.50- - - - - -Equation 2
- - - - - - - - - - - - - --

Substitute Method equation 1

x + y - 38

x + y - x = 38 - x

y = 38 - x

The answer is y = 38 - x

Insert the y value into equation 2

- - - - - - - - - - - - - - - - - - - -- -

9x + 12.50x = 415.50

9x + 12.50(38 - x ) = 415.50

9x + 475 - 12.50x = 415.50

- 3.5 x + 475 = 415.50

- 3.5x + 475 - 475 + 415.50 - 475

- 3.5 x + = - 59.5

- 3.5x /-3.5 = - 59.5 / - 3.5

x = 17

The answer is x = 17

Insert the x value into the equation 1

- - - - - - -- - - - - - - - - - - - - -- - - -

x + y = 38

17 + y = 38

17 + y - 17 = 38 - 17

y = 21

The answer is y = 21

Inaert the y value into equation 1

- - - - - - - - - - -- - - - - -- - - - -

Check for equation 1

x + y = 38

17 + 21 + 38

38 = 38

- - - - --

Check for equation 2

9x + 12.50 y 415.50

9(17) + 12.50(210 = 415.50

153 + 262.50 = 415.50

415.50 = 415.50

- - - - - - - - - - - -

The solution set { 17, 21 }

- - - - - - - - - - - -

annie ordered 17 small pizzas

and

21 large pizzas

- - - - - - - -s-

Answer 6

Here's how to do this problem Kassie. Let x = the number of small pizzas and y = the number of large pizzas. Now we know that x + Y = 38 and 9x + 12.5 y = 415.5. With these two equations you should be able to solve for both x and y. Good luck.

Answer 7

Let x be the number of small pizzas ordered. So (38-x) is the number of large pizzas ordered.

Balance by the total cost:
9x+12.5(38-x) = 415.5

Solve for x,
x = 17

Annie ordered 17 small pizzas.

Answer 8

Let x = Number of $9.00 pizzas
Then 38 - x = number of $12.50 oizzas
So 9x +12.5(38-x) = 415.50
9x + 475 -12.5x = 415.5
-3.5x = -59.5
x = 17 small pizzas
38-17 = 21 large pizzas

Answer 9

This is a problem that has to be solved using SIMULTANEOUS EQUATIONS:

The two equations you have to solve are:

x + y = 38
9x + 12.5y = 415.5

If you solve these equations simultaneously, you'll find that:

x =17 and y=21.