Question

Laura and luis are hosting a fifa world cup finals party and have purchased dinnerware to represent their favorite teams. Lara, a fan of team Germany, bought 25 cups and 40 plates with the German flag printed on them. Luis, who is rooting for Argentina, bought 20 cups and 35 plates with the Argentinian flag printed on them. Laura spent a total of $445.00 and Luis spent a total of $380.00

Answer 1

The system of equations representing the system is:

25c + 40p = 445

20c + 35p = 380

Step-by-step explanation:

In order to solve this problem, we call:

c = the price of one cup

p = the price of one plate

We know that:

- Lara bouthg 25 cups and 40 plates, and she paid a total of $445.00. So, this means that

25c + 40p = 445 (1)

- Luis bought 20 cups and 35 plates, and he paid a total of 380.00$. So, this means that

20c + 35p = 380 (2)

We can therefore solve the system of equations to find the price of each cup (c) and of each plate (p). By multiplying the first equation by 4 and the 2nd equation by 5 we get:

100c + 160p = 1780

100c + 175p = 1900

Substracting the 1st equation from the 2nd one,

15p = 120

Which gives

$p=\frac{120}{15}=8$

And substituting into (1),

$25c+40(8) =445\\25c=445-320\\25p = 125\\p = \frac{125}{25}=5$

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