Birdseed costs [tex][tex]$0.58 a pound and sunflower seeds cost $[/tex][/tex]0.88 a pound. Angela Leinenbachs' pet store wishes to make a 40
pound mixture of birdseed and sunflower seeds that sells for $0.76 per pound. How many pounds of each type of seed
should she use?
How many pounds of birdseed should Angela use?
13 pounds
(Simplify your answer.)



Answer :

osais

Answer:

Let's denote the pounds of birdseed as \( x \) and the pounds of sunflower seeds as \( y \). We need to set up and solve a system of equations based on the given information.

First, the total weight of the mixture is 40 pounds:

\[

x + y = 40

\]

Second, the total cost equation for the mixture, which should average $0.76 per pound, can be set up as:

\[

0.58x + 0.88y = 0.76 \times 40

\]

Simplify the second equation:

\[

0.58x + 0.88y = 30.4

\]

We now have the system of equations:

1. \( x + y = 40 \)

2. \( 0.58x + 0.88y = 30.4 \)

Solve the first equation for \( y \):

\[

y = 40 - x

\]

Substitute this into the second equation:

\[

0.58x + 0.88(40 - x) = 30.4

\]

Distribute the \( 0.88 \):

\[

0.58x + 35.2 - 0.88x = 30.4

\]

Combine like terms:

\[

-0.30x + 35.2 = 30.4

\]

Subtract 35.2 from both sides:

\[

-0.30x = -4.8

\]

Solve for \( x \):

\[

x = \frac{-4.8}{-0.30} = 16

\]

So, Angela should use 16 pounds of birdseed.

Now, find \( y \):

\[

y = 40 - x = 40 - 16 = 24

\]

Angela should use 16 pounds of birdseed and 24 pounds of sunflower seeds.

To verify, let's check the cost:

\[

0.58 \times 16 + 0.88 \times 24 = 9.28 + 21.12 = 30.4

\]

Thus, the calculations are correct. The simplified