Question

Help will fan and medal.
Use elimination
On the first day, a total of 40 items were sold for $356. Define the variables, and write a system of equations to find the number of cakes and pies sold. Solve by using elimination.

Answer 1

pies are 10 dollars cakes are 8

Answer 2

Let P be the number of Pies sold,
and let C be the number of cakes sold.

Then our information is telling us that the number of Pies and Cakes sold is 40.
\(\large\rm P+C=40\)

Okay with the first equation?
Make sense? :)

Answer 3

ok

Answer 4

If cakes are 8 each,
then if I multiply the `number of cakes` by `the price per cake`,
it gives me the total price for all the cakes: 8C.

We can do similar with the Pies to get the total price for all of the pies: 10P.

These totals add up to 356 dollars.
This gives us our second equation:
\(\large\rm 10P+8C=356\)

Answer 5

So that gives us a system of `two equations` which each involve `two unknowns`.

Answer 6

\[\large\rm P+C=40\]\[\large\rm 10P+8C=356\]

Answer 7

If we're going to use the `elimination method`,
then we need to match up one of the variables in both equations.

How bout the P's maybe?
How would we match them up?
We want to multiply the top equation by some value to match up the P's.
Any ideas? :)

Answer 8

multiply the top equation by 4?

Answer 9

If we multiply by 4,
that will give us 4P in the top equation.

Hmm we need to match them up. 4P doesn't match 10P.

Answer 10

ok how about -10?

Answer 11

Oo very nice.
So multiplying by 10 will match them up.
And the negative makes them opposite signs.

Answer 12

\[\large\rm -10P-10C=-400\]\[\large\rm ~~~10P+~~8C=~~~356\]So we've multiplied the top equation by -10 (both sides).
Now we can `add` these equations together.
What do you get? :)

Answer 13

C=$17.50
P=$22.50

Answer 14

Hmm

Answer 15

gtg bye

Answer 16

When you add the equations,
the P's cancel out.
And you're left with:\[\large\rm -2C=-44\]

Answer 17

oh ok :)