Question

Jambalaya is a Cajun dish made from chicken, sausage, and rice. Simone is making a large pot of jambalaya for a party. Chicken costs $6 per pound, sausage costs $3 per pound, and rice costs $1 per pound. She spends $42 on 13 and a half pounds of food. She buys twice as much rice as sausage.

Using a system of equations, how much sausage will Simone use in her dish?
a.4.5 lb of sausage
c.6 lb of sausage
b.3 lb of sausage
d.12 lb of sausage

Answer 1

this is the last question i have left to answer

Answer 2

Why am I feeling hungry all of a sudden after reading a math problem?

Answer 3

Let C be the number of pounds of chicken,
R be the number of pounds of Rice, and
S be the number of pounds of Sausage

Answer 4

C + R + S = 13.5
R = 2S
6C + 3S + R = 42
Solve the simultaneous equations for C, R and S.

Answer 5

Actually you just need to solve for S.

Answer 6

In order to have a system of equations in 2 variables, you have to use the fact that sausage is equal to twice the rice. So we have c = chicken, r = rice, and s = 2r. These combine in an amount to be 13 pounds of food and she spends $42. One equation will relate the pounds of food and the other the amount each costs per pound to what she spent. Adding the pounds of food together to equal 13 means you have c + r + 2r = 13 or c + 3r = 13. Using their cost per pound in relation to what was spent, you have
6c + 1r + 3(2r) = 42

Answer 7

This gives you a system of 2 equations now:
c + 3r = 13
6c + 7r = 42

Answer 8

Do you know how to solve that?

Answer 9

no

Answer 10

You could use the substitution method, which would be easiest here. Solve the first equation for c. What do you get? c = what?

Answer 11

c=3.18

Answer 12

would the answer be c?

Answer 13

IMStuck: You may want to recheck your equations. " She buys twice as much rice as sausage" implies r = 2s. I have given the three equations earlier.

Answer 14

Also, the total weight of the food is 13.5 pounds (not 13 pounds).

Answer 15

Gotcha! Misread it!

Answer 16

C + R + S = 13.5 (1)
R = 2S (2)
6C + 3S + R = 42 (3)

Put (2) in (1) and (3):
(1): C + 2S + S = 13.5. C + 3S = 13.5 (4)
(3): 6C + 3S + 2S = 42. 6C + 5S = 42 (5)

Multiply (4) by -6 and add it to (5):
-6C - 18S = -81
6C + 5S = 42
add
-13S = -39

S = 3 pounds.

Answer 17

And I have to say that your r = 2s is off. If she buys twice as much rice as sausage, she buys one quantity of sausage for every 2 quantities of rice, which implies 2r = s.

Answer 18

The rice is twice as much as sausage means more rice than sausage. So r = 2s.