Question

Hunter needs 12 ounces of a snack mix that is made up of seeds and dried fruit. The seeds cost $1.50 per ounce, and died fruit costs $2.50 per ounce. Hunter has $22 to spend and plans to spend it all.

Let x = the amount of seeds

Let y = the amount of dried fruit

Part 1: Create a system of eqution to represent the senario.

Part 2: Solve your system using any method (Desmos, Linear combination, or subsitution). Write your answer as an orderd pair.
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Answer 1

Part 1:

We are given that Hunter needs 12 ounces of snack mix made up of seeds and dried fruit, and has $22 to spend. Let x be the amount of seeds (in ounces) and y be the amount of dried fruit (in ounces).

The total amount of snack mix is 12 ounces, so we have:

x + y = 12

The cost of the snack mix is $22, and the cost per ounce of seeds and dried fruit are $1.50 and $2.50, respectively. Therefore, we have:

1.5x + 2.5y = 22

This gives us a system of two equations:

x + y = 12

1.5x + 2.5y = 22

Part 2:

We can solve this system using substitution. Rearranging the first equation, we have:

x = 12 - y

Substituting this expression for x into the second equation, we get:

1.5(12 - y) + 2.5y = 22

Expanding and simplifying, we get:

18 - 1.5y + 2.5y = 22

y = 4

Substituting this value of y into the expression for x, we get:

x = 12 - y = 12 - 4 = 8

Therefore, Hunter needs 8 ounces of seeds and 4 ounces of dried fruit to make 12 ounces of snack mix, and will spend $1.50(8) + $2.50(4) = $20 on the snack mix.

As an ordered pair, the solution is (8,4).

Answer 2

Answer: (18, 4)

Part 1:

The cost of seeds and dried fruit together is $22:

1.5x + 2.5y = 22

Hunter plans to spend all of his money on seeds and dried fruit:

x + y = 22

Part 2:

We can use substitution method to solve the system of equations:

x = 22 - y (from the second equation)

1.5(22 - y) + 2.5y = 22 (substitute x into the first equation)

33 - 1.5y + 2.5y = 22

y = 4

Substituting y = 4 into x + y = 22, we get x = 18.

Therefore, the ordered pair representing the number of seeds and dried fruit that Hunter bought is (18, 4).