Story Problem

Question

A student spent a total of 18 hours one week studying for three courses: biology, English, and history. Twice the time was spent studying English equals the time spent studying biology and history combined. How much time (hours and minutes) did she spend studying each subject?

Answer 1

Hi Alissa.

 

Need to assign each course a letter name, so lets say that we will use

 

E=English, B=biology, and H=History

 

These letters actually represent the time that the student spent studying that subject.

 

"Twice the time was spent studying English" converts in "math speak" to

2E

 

"equals" clearly translates to

=

 

"the time spent studying biology and history combined"

The key here is the word "combined". This means ADD.  So this part translates to

B+H

 

All together, these become

2E=B+H

 

The last thing we need is the first sentence which says 

"spent a TOTAL of 18 hours"  so that means we need to add all of these up, and that sum must equal 18

 

So B+H+E=18

 

We know that 2E=B+H, so we can replace "B+H" with "2E" and get

 

(B+H) + E = 18

   2E    +  E = 18

 

Simplifying we get

 

3E=18

 

Divide both sides by 3 and get 

 

E = 6 or the student spent 6 hours studying English.

 

So B+H=2*6=12

 

We would need more information to know how these 12 hours are split up between history and biology.