MATH SOLVE

4 months ago

Q:
# Jimmy has studied 22 hours over the last 10 days for the ACT. He studied either 2 hours a day or 3 hours a day. During the 10 day period, how many days did Jimmy study for three hours a day? A) 1 B) 2 C) 3 D) 4

Accepted Solution

A:

Let x represent the # of 2-hour days and y the # of 3-hour days. Jimmy's study was spread over 10 days. Thus, x + y must sum up to 10. Also, 2x + 3y must sum up to 22 hours.

Our system now looks like this:

x + y = 10

2x + 3y = 22

Multiply the first equation by -2: -2x - 2y = -20

Add the 2nd equation to this:

-2x - 2y = -20

2x + 3y = 22

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

y = 2 So Jimmy had 2 3-hour study days and 8 2-hour study days.

Note how these figures add up to 22: 6 + 16 = 22

Our system now looks like this:

x + y = 10

2x + 3y = 22

Multiply the first equation by -2: -2x - 2y = -20

Add the 2nd equation to this:

-2x - 2y = -20

2x + 3y = 22

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

y = 2 So Jimmy had 2 3-hour study days and 8 2-hour study days.

Note how these figures add up to 22: 6 + 16 = 22