SOLUTION: the question reads: Toy World, a retail chain, placed a seasonal order for stuffed animals from a distributor. Large animals cost $20.00 and small ones cost $14.00. a)If the tota

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Question 74678This question is from textbook Contemporary Mathematics
: the question reads: Toy World, a retail chain, placed a seasonal order for stuffed animals from a distributor. Large animals cost $20.00 and small ones cost $14.00.
a)If the total cost of the order was $7,320 for 450 pieces, how many of each size were ordered?
b)What was the dollar amount of each size ordered?
This is what I know:
x=Large animals at a cost of $20.00/piece
y=Small animals at a cost of $14.00/piece
450 pieces were ordered
$7320 is the total cost of order
so I think my equation should read: 20x+14y/450=$7320
Is this right? If so can you please help me with the solution.
Thank you so much for you help! This question is from textbook Contemporary Mathematics

Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
Let L=# of large animals and s=# small animals (it's easier to recognize L and s compared to x and y). Since we know they ordered 450 pieces of both large and small animals the first equation looks like

And since the total price is $7,320 it is
the number of animals multiplied by their respective prices add up to the total.
Solve for L. Plug this ito

So they ordered 280 small animals. Use this to solve for L

So they ordered 170 large animals.

Check:

Plug in L=170 and s=280

We can see the values satisfies the system of equations:
works
works

Here's another way to do it

Solved by pluggable solver: Linear System solver (using determinant)

Solve:

Any system of equations:

has solution

or

(L=170, s=280}