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Walnuts, peanuts, and chocolate chips are mixed composed in a ratio of 7:2:5. What is the weight of the mixture if 2.5 lbs of chocolate chips were used for making it?

Please show your work!

Respuesta :

metchelle
Here is the answer. In order for us to know the weight of the mixture, we are going to solve for the weight of each first. Given that the weight of the chocolate chips is 2.5 and the ratio given is 7:2:5. First, let us solve for 2:5. So, ? : 2.5. The answer would be 1. So the weight of the peanuts is 1 pound. Now, we are going to solve for 7:2 given that the peanuts weigh 1 pound. 7:2 :: ? : 1 And the answer is 3.5. Therefore the weight of the walnuts is 3.5 pounds. So the weight of the mixture is 7 pounds. Hope this helps.
calculista

Answer:

The weight of the mixture is equal to [tex]7\ lb[/tex]

Step-by-step explanation:

Let

x-----> the weight of walnuts

y----> the weight of peanuts

z----> the weight of chocolate chips

we know that

[tex]\frac{x}{y}=\frac{7}{2}[/tex] -----> equation A

[tex]\frac{x}{z}=\frac{7}{5}[/tex] -----> equation B

[tex]\frac{y}{z}=\frac{2}{5}[/tex] -----> equation C

[tex]z=2.5\ lb[/tex]

Step 1

Substitute the value of z in the equation B and solve for x

[tex]\frac{x}{2.5}=\frac{7}{5}[/tex]

[tex]x=2.5*7/5=3.5\ lb[/tex]

Step 2

Substitute the value of z in the equation C and solve for y

[tex]\frac{y}{2.5}=\frac{2}{5}[/tex]

[tex]y=2.5*2/5=1\ lb[/tex]

Step 3

Find the weight of the mixture

we know that

The weight of the mixture is equal to

[tex]x+y+z[/tex]

substitute

[tex]3.5\ lb+1\ lb+2.5\ lb=7\ lb[/tex]


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