The cost of four large plans and eight medium plans is $40. The cost of five large plants and two medium plans is $28. What is the cost of large plants and medium plants .

Answer 1

Hi Grant,

I'm assuming the "plans" means plants. If so, here's the solution

1. Lets set variables

x = the cost of large plants

y = the cost of medium plants

2. Create a system of equations.

4x+8y = 40 eq1

5x+2y = 28 eq2

3. Solve the system of equations. There are two different methods to solve these equations. Either by elimination or substitution. Since the least common multiple (LCM) is small, elimination is an easier method.

4. Multiply the second equation by 4 to achieve the LCM

4x+8y = 40

20x+8y = 112

5. Perform elimination (subtract the 2nd equation by the first)

4x+8y=40

-20x-8y=-112

-16x=-72

x= $4.50 is the cost of each large plant

6. Substitute the answer for x into either equation 1 or equation 2 to find the cost of medium plants. I suggest substituting into equation 1 to make the math easier.

4x+8y=40

4(4.5)+8y = 40

18+8y = 40

8y = 22

y = 22/8 o=11/4 = $2.75 is the cost of each medium plant

7. Double check the answer to see if it makes sense. We can plug our answer for x and y into the first equation to see if the left hand side of the equation is equal to 40. If it does, we know the solution is correct

4x+ 8y=40

4(4.5)+8(2.75) =40

Our solution is correct!