Answer:
The cost of one bag of windflower is [tex]11\[/tex] and one bag of crocus is [tex]16\[/tex]
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. [tex]5x+6y=151[/tex]
[tex]6y=151-5x ----- (1)[/tex]
Sales by Shanice is 4 bags of windflower bulbs and 3 packages of crocus bulbs is 92,
i.e. [tex]4x+3y=92 ----- (2)[/tex]
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.
[tex]\therefore[/tex]multiplying (2) by 2 on both sides we get,
[tex]2\times(4x+3y)=2\times92[/tex]
[tex]8x+6y=184[/tex]
[tex]6y=184-8x ----- (3)[/tex]
On equating (1) and (3) we get,
[tex]184-8x=151-5x[/tex]
On grouping the terms,
[tex]184-151=-5x+8x[/tex]
[tex]33=3x[/tex]
[tex]x=\frac{33}{3}[/tex]
[tex]x=11[/tex]
On substituting the value of x in (2) we get,
[tex]4\times11+3y=92[/tex]
[tex]44+3y=92[/tex]
[tex]3y=92-44[/tex]
[tex]3y=48[/tex]
[tex]y=\frac{48}{3}[/tex]
[tex]y=16[/tex]
Hence, the cost of one bag of windflower bulb is 11 and one bag of crocus bulb is 16.
