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Maria is making trail mix to sell for a fundraiser. She wants to use a nut mix that is 10% peanuts and another that is 50% peanuts. She wants to make 40 pounds of that mix that is 25% peanuts. How much of each type should she use?

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ukshedrack

Answer:

Amount of pounds for nut mix 1 = 25

Amount of pounds for nut mix 2 = 15

Step-by-step explanation:

Let the amount of pounds for nut mix 1 = x

and amount of pounds for nut mix 2 = y

Amount of total mixture = 40 pounds

So, x + y = 40 ... Equation 1

10% peanuts for nut mix 1 = 0.1*x = 0.1x

50% peanuts for nut mix 2 = 0.5*y = 0.5y

25% peanuts for the mixture = 0.25*40 = 10

So, 0.1x + 0.5y = 10 ... Equation 2

So, we have the system of equations

x + y = 40 ... Equation 1

0.1x + 0.5y = 10 ... Equation 2

Multiply equation 1 by 0.1

0.1x + 0.1y = 40*0.1 = 4 ... Equation 3

We then have,

0.1x + 0.5y = 10 ... Equation 2

0.1x + 0.1y = 4 ... Equation 3

Subtract equation 3 from equation 2

0.1x - 0.1x + 0.5y - 0.1y = 10 - 4

0.4y = 6

Divide both sides by 0.1

0.4y/0.4 = 6/0.4

y = 15 pounds

Use y = 15 in equation 1

x + 15 = 40

x = 40 - 15

x = 25 pounds

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