Question

A landscaping company sells trees for $25 each and flowers for $5 each. Dillon has $125 dollars to spend

on plants for his yard. Write an equation in standard form to represent the situation. Dillon decides he should
buy all of one type of plant, trees or flowers. How many trees can he afford and how many flowers can he
afford if he buys all of one type?

Answer 1

5x + y = 25

Dillon can buy 25 flowers.

Dillon can buy 5 trees

Explanation:

Equations

The standard form of a linear equation is:

ax + by = c

Where a, b, and c are constants, and x, y are the variables.

Given the conditions of the problem, we'll build the equation that represents the situation.

Let's call:

x=number of trees

y=number of flowers

Since the landscaping company sells trees for $25 each and flowers for $5 each, buying x trees and y flowers cost:

25x+5y dollars

Knowing Dillon has $125 to spend, then:

25x + 5y = 125

Dividing by 5:

5x + y = 25

This is the equation that models the situation.

If Dillon decides to buy only one type of plant, then the other must be set to zero.

If he buys only flowers, then x=0. Solving for y:

5(0) + y = 25

y = 25

Dillon can buy 25 flowers.

If he buys only trees, then y=0. Solving for x:

5x + 0 = 25

x = 5

Dillon can buy 5 trees