Answer:
A bag of crocus bulbs costs $15
Step-by-step explanation:
Assume that x is the cost of a bag of windflower bulbs and y is the cost of a package of crocus bulbs
∵ The cost of a bag of windflower bulbs is $x
∵ The cost of a package of crocus bulbs is $y
∵ Eugene sold 14 bags of windflower bulbs and 5 packages
of crocus bulbs for a total of $257
- Multiply x by 14 and y by 5, then equate the sum of the
products by 257
∴ 14x + 5y = 257 ⇒ (1)
∵ Scott sold 11 bags of windflower bulbs and 1 package of
crocus bulbs for a total of $158
- Multiply x by 11 and y by 1, then equate the sum of the
products by 158
∴ 11x + y = 158 ⇒ (2)
Now we have a system of equations to solve it
Multiply equation (2) by -5 to make the coefficients of y equal in value and opposite in signs
∵ -55x - 5y = -790 ⇒ (3)
- Add equations (1) and (3) to eliminate y
∴ -41x = -533
- Divide both sides by -41
∴ x = 13
Substitute the value of x in equation (1) or (2) to find y
∵ 11(13) + y = 158
∴ 143 + y = 158
- Subtract both sides by 143
∴ y = 15
A bag of crocus bulbs costs $15
