Question

Help me ill give 100 pts

Answer 1

Small pizza is for 1 person, Large pizza is for 5 people

Skills needed: System of Equations

Explanation:

1) First, let's make two variables:

--> = how many people a large pizza can feed

--> = how many people a small pizza can feed

2) We need to use a system of equations to solve this --> A system is 2 or more equations with specific solutions for the variables involved.

Example:

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

We can solve with elimination:

(Rewriting the first equation to look like the second one)

---> Then we add both:

When we add both equations, we eliminate the variable , solving for easily. After this, we can solve for

--->

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

This is the elimination method of a system (Note: we can also subtract equations if needed)

3) Let's make a system for this problem:

---> 3 small pizzas (multiplied by the number of people it can feed) + 2 large pizzas (multiplied by the number of people it can feed) is for 13 people.

---> 3 small pizzas (multiplied by the number of people it can feed) + 4 large pizzas (multiplied by the number of people it can feed) is for 23 people.

4) We have two equations:

We can eliminate by subtracting both equations.

--->

We subtracted from which is just 0 (so it does not have to be shown)

We subtracted from which is just

On the right side: subtracted from which is just

----> , divide by -2,

, which means a large pizza is for 5 people.

Substituting into the first equation (it does not matter which one you substitute into) will get

Small pizza is for 1 person.

Answer 2

Small pizza is for 1 person, Large pizza is for 5 people

Skills needed: System of Equations

Explanation:

1) First, let's make two variables:

-->
`l` = how many people a large pizza can feed

-->
`s` = how many people a small pizza can feed

2) We need to use a system of equations to solve this --> A system is 2 or more equations with specific solutions for the variables involved.

Example:

`y=x+5`

`y+x=10`

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

We can solve with elimination:

`y-x=5 \\ y+x=10`

(Rewriting the first equation to look like the second one)

---> Then we add both:

`y-x=5 \\ y+x=10 \\ 2y=15 \\ y= 7.5`

When we add both equations, we eliminate the variable
`x`, solving for
`y` easily. After this, we can solve for

--->
`y+x=10 \\ 7.5+x=10 \\ x=2.5`

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

This is the elimination method of a system (Note: we can also subtract equations if needed)

3) Let's make a system for this problem:

`3s+2l=13` ---> 3 small pizzas (multiplied by the number of people it can feed) + 2 large pizzas (multiplied by the number of people it can feed) is for 13 people.

`3s+4l=23` ---> 3 small pizzas (multiplied by the number of people it can feed) + 4 large pizzas (multiplied by the number of people it can feed) is for 23 people.

4) We have two equations:

`3s+2l=13 \\ 3s+4l=23`

We can eliminate
`s` by subtracting both equations.

--->
`3s+2l=13 \\ 3s+4l=23 \\ -2l=-10 \\ l=5`

We subtracted
`3s` from
`3s` which is just 0 (so it does not have to be shown)

We subtracted
`4l` from
`2l` which is just
`-2l`

On the right side:
`23` subtracted from
`13` which is just
`-10`

---->
`-2l=-10`, divide by -2,
`-10 / -2 = 5`

`l=5`, which means a large pizza is for 5 people.

`3s+2l=13 \\ 3s+2(5)=13 \\ 3s+10=13 \\ 3s=3 \\ s=1`

Substituting
`l` into the first equation (it does not matter which one you substitute into) will get
`s=1`

Small pizza is for 1 person.