Kathryn H. answered • 04/28/21
Current Master's Student Looking to Tutor in Math!
Hello Silvio!
The first step to this type of problem is to identify our variables and write a system of equations. Let's use h for the cost of one hostas, and g for the cost of one bunch of ornamental grass. Since Elisa bought 8 hostas and 4 bunches of ornamental grass for a total of 76$, we can represent this by the equation:
8h + 4g = 76
Ming bought 8 hostas and 7 bunches of ornamental grass for a total of 97 dollars. We can represent this by the equation:
8h + 7g = 97
The problem wants us to solve the system of equations using substitution. The substitution method has us solve one of the equations for a variable, and then plug the result in to the other equation for that variable. We can pick either equation and either variable, so let's solve the first equation 8h + 4g = 76 for g.
8h + 4g = 76
4g = 76 - 8h Here I subtracted 8h from both sides.
g = 19 - 2h Here I divided each term by 4.
Now that we know g = 19 - 2h, we can plug 19 - 2h in to the other equation for g.
Our other equation is 8h +7g = 97
8h + 7(19-2h) = 97 Now we only have one variable h, so we can solve for it!
8h + 133 - 14h = 97 Here I multiplied 7 by each term in the parentheses.
-6h + 133 = 97 Here I added 8h and -14h to get -6h.
-6h = -36 Here I subtracted 133 from both sides
h = 6 Here I divided both sides by -6.
The cost of one hostas is 6$.
Now that we know h = 6, we can plug this in to either of our original equations and solve for g. We already solved one of our original equations to be g = 19 - 2h which will be the easiest to work with.
g = 19 - 2(6) Here I plugged in h = 6.
g = 19 -12 Here I multiplied 2 by 6.
g = 7 Here I subtracted 19 - 12.
The cost of one bunch of ornamental grass is 7$.
Good luck on your homework!
Katie
