Question

an online seed supplier packages a seed mix that costs the company 20.70$ per pound the mix includes poppy seeds costing 24$ per pound and clover seeds costing 13.00$ per pound if a worker is going to prepare some of this mix and has already measured out 26 pounds of poppy seeds what quantity of clover seeds should be added?​

Answer 1

11.14 pounds ( approx )

Explanation:

Let x pounds of poppy seeds and y pounds of clover seeds were mixed,

∵ Poppy seed costs 24$ per pound and clover seed costs 13.00$ per pound,

Thus the total cost of x pounds of poppy seeds and y pounds of clover seeds = 24x + 13y,

According to the question,

Resultant mixture costs $ 20.70 per pound,

∴ Total cost = 20.70(x+y),

`\implies 24x + 13y = 20.70(x+y)`

`24x + 13y = 20.70x + 20.70y`

`24x - 20.70x = 20.70y - 13y`

`3.3x = 7.7y`

`\implies y = (3.3)/(7.7)x=(3)/(7)x`

If x = 26,

`y=(3)/(7)* 26=(78)/(7)=11.1428571429\approx 11.14`

Hence, 11.14 pounds of clover seeds should be added.

Answer 2

The quantity of clover seeds in pounds to be added is 11.14

Explanation:

Let

x -----> the quantity of poppy seeds in pounds

y -----> the quantity of clover seeds in pounds

we know that

`24(x)+13(y)=20.70(x+y)` -----> equation A

`x=26\ pounds` ----> equation B

substitute equation B in equation A and solve for y

`24(26)+13(y)=20.70(26+y)`

`624+13y=538.2+20,70y`

`20.70y-13y=624-538.2`

`7.7y=85.8`

`y=11.14\ pounds`

therefore

The quantity of clover seeds in pounds to be added is 11.14