Hi Paola,
First you want to highlight and separate relevant information. Organize the items by the person who bought them. Since there are only 2 items being bought, we can assign a variable or letter to each item:
Shayna
Grass: 5ft^2 (let's call grass X)
Geraniums: 10 (let's call geraniums Y)
Total cost: $175
Brenda
Grass: 9ft^2 (let's call grass X)
Geraniums: 4 (let's call geraniums Y)
Total cost: $147
Now that you have separated the information, you can write 2 equations, one for Shayna and one for Brenda:
Shayna
5x + 10y = $175
Brenda
9x + 4y = $147
Notice how the numbers stayed the same, but I dropped the units and replaced them with X or Y depending on what we assigned. Now we can begin to solve. We want to isolate one of the variables (either X or Y, the order does not matter). In order to do that, let's choose one of the equations to use, and one of the variables to isolate. Again, you can start with whatever you want, as long as you did the math correctly you should get the same answer no matter how you do it.
I will isolate the x from Shayna's equation. Below are the steps:
1) 5x + 10y = $175 (rewrite the equation)
2) 5x = $175 - 10y (subtract the 10y to the other side since we are trying to isolate x, again, you can do y first if you would like. This is just how I did it)
3) (5x)÷5 = ($175 - 10y)÷5 (divide both sides of the equation by 5)
4) (5x/5) = ($175/5) -(10y/5) ---> x = $35 - 2y (simplify the equation, you have now isolated x and can plug it into the equation which you have not yet used, in this case, Brenda's equation)
5) 9x + 4y = $147 ---> 9($35 - 2y) + 4y = $147 (now you have plugged in the calculated value of x into the new equation. The only variables in this equation are y's so now you can solve for y, which stands in place for the geraniums)
6) $315 - 18y + 4y = $147 (distribute the 9 to the quantity in the parenthesis)
7) $315 - $147 = 18y - 4y (subtract $147 to the left side, subtract 4y to the right side, add 18y to the right side)
8) $168 = 14y ---> y = $12 (solve for y)
Now that you have solved for the value of geraniums, use that number (y) to plug into all of the y variables in either equation. Since we just finished using Brenda's equation, I prefer to switch back to Shayna's equation to avoid plugging something back into the same equation. This is a good habit for higher level maths becuase sometimes that can lead you to go in circles.
9) 5x + 10y = $175 ---> 5x + 10($12) = $175 ---> 5x + $120 = $175 (plug in the value of y = $12 into Shayna's equation)
10) 5x = $175 - $120 ---> 5x = $55 ---> x = $11 (subtract $120 to the right side, simplify)
Now you know the cost of x which stands in for 1ft^2 of grass. Therefore:
$11/ft^2 of grass, $12/geranium
Hope this helps!
Best,
Kalvin
