****First part of the problem: Each broccoli plant needs 12 inches of space and each pea plant needs 6 inches of space. The row is 10 feet (120 inches) long.
You can use whatever letter you wish but I like to try to match the letters so I can easily determine what I am dealing with. For this example, we will use B=broccoli and P=Pea.
12(B) + 6(P) = 120 This equestion translates what the first problem states. Since all the units of measure are already in inches, we do not need to convert anything. So it states that broccoli needs 12 inches [hence the 12(B)] we use the letter 'B'
since we do not know the number of broccoli plants. It also states that the pea plants takes 6 inches [hence 6(P)] we use the letter 'P' since we do not know the number of pea plants. Both added together will 120 inches.
****Second part of the problem: If you want a total of 13 plants
So this tells me when I add the number of broccoli (B) plus the number of pea (P) plants, I should have a total of 13 hence B+P=13.
I have two equations: 12(B) + 6(P) = 120
Decide which one you wish to solve first which can be either Broccoli or Pea. We will solve for Broccoli (B) so in the equation B+P=13, we will subtract 'P' from both sides.
B + P = 13
B = 13 - P This is what we are left with after subtracting 'P' from both sides. Now in the other equation we will substitute this equation into the 'B' which will look like this:
12(B) + 6(P) = 120 B = 13 - P
[12(13-P)] +6P=120 Now we just multiply it out. I inserted brackets just so u know that the first part is seperate from the 6p. so we multiply 12*13 and 12*(-P) and we get the following:
156-12P+6P=120 We will now add the like terms together so the -12P+6P = -6P which gives us:
156-6P=120 Since we want to get the letter on one side, we will subtract 156 from both sides
so we will have -6P=120-156 which will leave us with:
-6P=-36 We divide by -6 (negative six) on both sides which will leave 'P' by itself
P=-36/-6 36 divided by 6 =6. since both numbers are negative we get a positive number
So P=6 Now to check our work, we will plug this number into the total number of plants equation
B=13-P B=13-6 B=7 So B=7 & P=6
So now lets plug in these numbers into the other equation: 12(B) + 6(P) =120
12(B) + 6(P) = 120 12(7) + 6(6) =120 84+36=120 120=120
B+P=13 7 + 6 =13 13=13
Our figures are correct since both equations work out with our solution.