Question

Jacob and Sarah are saving money to go on a trip. They need at least $1850 in order

to go. Jacob mows lawns and Sarah walks dogs to raise money. Jacob charges $15
each time he mows a lawn and Sarah charges $10 each time she walks a dog. The
number of dog walks that Sarah has scheduled is no more than five times the
number of lawns Jacob has scheduled to mow. Sarah will walk at least 65 dogs.

Answer 1

`\textsf{Constraint 1}: \quad 15x+10y\geq 1850`

`\textsf{Constraint 2}: \quad y \leq 5x`

`\textsf{Constraint 3}: \quad y \geq 65`

Explanation:

Inequality signs:

• < Less than.
• ≤ Less than or equal to.
• > More than.
• ≥ More than or equal to.

Given variables:

• x = Number of lawns mowed.
• y = Number of dogs walked.

Constraint 1

Given information:

• $15 = Charge for mowing a lawn.
• $10 = Charge for walking a dog.
• $1850 = Minimum amount needed for the trip.

Therefore, the amount earned from mowing the lawns and walking dogs should be more than or equal to $1850:

`\boxed{15x+10y\geq 1850}`

Constraint 2

Given information:

• The number of dog walks that Sarah has scheduled is no more than 5 times the number of lawns Jacob has scheduled to mow:

Therefore, Sarah will walk less than or equal to 5 times the number of lawns mowed:

`\boxed{y \leq 5x}`

Constraint 3

Given information:

• Sarah will walk at least 65 dogs.

Therefore, Sarah will walk more than or equal to 65 dogs:

`\boxed{y \geq 65}`