Question

Otis and Rhonda need 14 ounces of a snack mix that is made up of seeds and dried

fruit. The seeds cost $1.50 per ounce and dried fruit costs $2.50 per ounce. Otis
and Rhonda have $24 to spend and they plan to spend it all.
Let x = the amount of seeds
Let y = the amount of dried fruit
Part 1: Create a system of equations to represent the scenario. (2 points)
Part 2: Solve your system using any method. Write your answer as an ordered Pair.

Answer 1

A)

x + y = 14

1.5x + 2.5y = 24

B) (11,3)

Explanation:

x + y = 14

1.5x + 2.5y = 24

x = 14 - y

1.5(14 - y) + 2.5y = 24

21 - 1.5y + 2.5y = 24

y = 3

x = 14 - 3

x = 11

Answer 2

(11, 3)

Explanation:

Let's say that the ounces of seeds is x and the ounces of dried fruit is y. Since Otis and Rhonda need 14 ounces total: x + y = 14.

Each ounce of seeds is 1.50 and each ounce of dried fruit is 2.50. In total, they will add up to 24, so: 1.50x + 2.50y = 24

Part 1

The system is:

x + y = 14

1.50x + 2.50y = 24

Part 2

To solve, we can use substitution. First, subtract x from both sides of the first equation: x + y - x = 14 - x ⇒ y = 14 - x

Now, we can substitute this in for y in the second equation:

1.50x + 2.50 * (14 - x) = 24

1.50x + 35 - 2.50x = 24

-x + 35 = 24

x = 11

Plug 11 into the equation x + y = 14 to solve for y:

11 + y = 14 ⇒ y = 3

Thus, the answer is (11, 3).

Hope this helps!