Answer to Question #249245 in Linear Algebra for Riri

Question

At the beginning of a new semester, Andy makes plans for a successful semester. He allocates 42 hours per week for study time for the four courses he is taking: Math, English, Chemistry and History He decides to allocate half of his time to Math and English, and twice as much time to Math as to English. He decides to allocate twice as much to English as to History (a) Find a system of equations that represents this information. ( ) Solve the system to determine the number of hours allocated to each subject.

Answer 1

Let he allocates x hours for English, y hours for mathematics, z hours for chemistry and t hours for history.

x + y + z + t = 42 as total hours allocated is 42 hours .

x+y = 21 as he allocates half of his time to Math and English.

y = 2x as he allocates twice as much time to Math as to English.

x = 2t as he allocates twice as much time to English as to history.

So the system of equations are

x+y+z+t = 42 ---------------(1)

x+y = 21 ----------------(2)

2x - y = 0 ----------------(3)

2t - x = 0 ----------------(4)

Adding equation (2) and (3) we get

3x = 21 => x = $\frac{21}{3} = 7$

So y = 2*7 = 14

From equation (4)

2t = 7 => t = $\frac{7}{2} = 3.5$

From equation (1)

z = 42 - 7 - 14 - 3.5

=> z = 17.5

So he allocates 7 hours for English, 14 hours for mathematics, 17.5 hours for chemistry and 3.5 hours for history.