Question

Dan and shanice are selling flower bulbs for a school fundraiser. Customers can buy bags of windflower bulbs and packages of crocus bulbs. Dan sold 5 bags of windflower bulbs and 6 packages of crocus bulbs for a total of $151. Shanice sold 4 bags of windflower bulbs and 3 packages of crocus bulbs for a total of $92. What is the cost each of one bag of windflower bulbs and one package of crocus bulbs?

Answer 1

The cost of one bag of windflower is
`11\` and one bag of crocus is
`16\`

Solution:

Let windflower bulbs be x and crocus bulbs be y.

Sales by Dan is 5 bags of windflower bulbs and 6 packages of crocus bulbs for 151,

i.e.
`5x+6y=151`

`6y=151-5x ----- (1)`

Sales by Shanice is 4 bags of windflower bulbs and 3 packages of crocus bulbs is 92,

i.e.
`4x+3y=92 ----- (2)`

Here we are eliminating the value of y so that we can find the value of x,

The least common multiple of the coefficients of y (6 and 3) is 6.

`\therefore`multiplying (2) by 2 on both sides we get,

`2*(4x+3y)=2*92`

`8x+6y=184`

`6y=184-8x ----- (3)`

On equating (1) and (3) we get,

`184-8x=151-5x`

On grouping the terms,

`184-151=-5x+8x`

`33=3x`

`x=(33)/(3)`

`x=11`

On substituting the value of x in (2) we get,

`4*11+3y=92`

`44+3y=92`

`3y=92-44`

`3y=48`

`y=(48)/(3)`

`y=16`

Hence, the cost of one bag of windflower bulb is 11 and one bag of crocus bulb is 16.