Math problem about systems of equations.

Question

i have to do this retarded summer math packet there's this one word problem i can't figure out.

write a system of equations and solve. Be sure to define the variables used. Megan exercises every morning for 40 minutes. She does a combination of step aerobics, which burns 11 Calories per minute, and stretching, which burns 4 Calories per minute. Her goal in to burn 335 Calories during her routine. How long should she spend on each type of exercise to reach her goal.

thanks so much!!

Answer 1

Okay you have to make 2 equations to solve.  The minutes of step aerobics will be a.  Stretching will be s.

She wants to burn 335 calories so:

11a+4s=335

She excercises for 40 total minutes so:

a+s=40

a=-s+40

Substitute:

11(-s+40)+4s=335

-11s+440+4s=335

-7s=-105

s=15

Since a+s=40, a=25 minutes

Answer 2

Let:

Total calories burned = C = 11(X) + 4(Y) <== (Equation #1)

where X = time spent doing step aerobics in minutes

........ Y = time spent stretching in minutes

Total workout time = T = X + Y <== (Equation #2)

They tell you that she exercises every morning for 40 minutes.  So they are telling you that T = 40 minutes.... which means that X + Y = 40 minutes

They also tell you that her goal is to burn 335 Calories.  So they are also telling you that C = 335 calories.... which means that 11(X) + 4(Y) = 335 calories....

Two equations, and two unknowns.... so you can solve for both "X" and "Y"....

Here are your two equations again....

X + Y = 40 <=== Equation 1

11X + 4Y = 335 <==== Equation 2

You can rewrite X + Y = 40 as..... Y = 40 - X.....

Now substitute the "40 - X" for "Y" in the 2nd equation....

11X + 4Y = 335 .... becomes...

11X + 4(40-X) = 335 .... now distribute the "4".... and you get....

11X + (4)(40) + (4)(-X) = 335

11X + 160 - 4X = 335 ... combine the 11X and the -4X.... and you get...

7X + 160 = 335

Now subtract "160" from both sides... like this...

7X + 160 = 335

.... - 160 .. -160

--------------------------

7X + 0 = 175

Now divide both sides by "7"... like this...

7X .. 175

---- = ------

7 ...... 7

The 7's on the left side cancel each other out... leaving you with..

X = 175 / 7 = 25 minutes...

So you just found out that X = 25 minutes... which means that she should spend 25 minutes doing step aerobics.....

They told you that she exercises 40 minutes.... so that X + Y = 40

So if she exercises 40 minutes and she spent 25 minutes doing step aerobics... that means that the remaining 15 minutes, she was stretching...  because 40 - 25 = 15 minutes....

So.... X = 25 minutes.... Y = 15 minutes....

To reach her goal of burning 336 calories.... Megan has to do:

25 minutes --- step aerobics

15 minutes --- stretching