I am having problems with a word problem. Here's the question...?

Question

A pet store owner mixes two types of bird seed that cost $1.25 per pound and $2.20 per pound to make 20 pounds of mixture that cost $1.65 per pound. How many pounds of each kind of birdseed are in the mixture?

Answer 1

Number of pounds of type A, costing $1.25/pound = x
Number of pounds of type B, costing $2.20/pound = y

The price of the mixture must be $1.65/pound.
Therefore 20 pounds must cost 20 * $1.65 = $33:

(x * 1.25 + y * 2.20) = 33

The total amount of seed mixture is 20 pounds:

x + y = 20

Solve:

x + y = 20 -> x = 20 - y

Substitute into (x * 1.25 + y * 2.20) = 33

(((20 - y) * 1.25) + (y * 2.20)) = 33
-> (20 * 1.25) - (y * 1.25) + (y * 2.20) = 33
-> 25 + (2.20-1.25) y = 33
-> 25 + 0.95 y = 33

Subtract 25 from both sides:

0.95 y = 8
-> y = 8/0.95
-> y = 8.42 pounds

Substitute into x + y = 20

x + 8.42 = 20
-> x = 20 - 8.42 = 11.58 pounds

Check in (x * 1.25 + y * 2.20) = 33

11.58 * 1.25 + 8.42 * 2.20 = 33

Therefore there are 11.58 pounds of type A and 8.42 pounds of type B in the mixture.

Answer 2

Let x = the number of pounds that cost 1.25/pound
20-x = the number of pounds that cost 2.20/pound, So 1.25x + 2.2(20-x) = (1.65)(20)
1.25x +44 - 2.2x =33
-.95x = -11
x= 11/.95 = 11 11/19 pounds @ $1.25/lb
20-x = 8 8/19 pounds @ $2.20/lb

Answer 3

Let the two amounts be x pounds and y pounds.

Can you now write either of the equations yourself?

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There is 20 pounds altogether, and so x + y = 20


Now the total value is 20*165 cents, so if you write down the total value of x pounds at 125c per pound and y pounds at 220c per pound, and put that equal to 20*165 you have the second equation. Can you solve these two simultaneous equations? I think the answers aren't particularly nice. (maybe 11.57 and 8.43 approx.) Are you sure the second price wasn't $2.25 instead of $2.20?

Answer 4

Build two equations where x and y are the number of pounds of each type of seed.

Hints to build the two equations:
- The total must be 20 pounds
- The total price must be $33.00 (20 pounds @ $1.65 per)

Answer 5

Here is a way to solve it with one variable.

you know it is 20 lbs.

1.25(20-x) + 2.2(x) = 33

1.65 X 20 is 33.00

25 - 1.25x + 2.2x = 33

.95x = 7

x = 7.368 lbs of the $2.20

12.631 of the $1.25

Answer 6

1.25 (x) + 2.20 (20-x) = 1.65(20)
.95x = 11
x=11.57 lbs
20-x = 8.42 lbs