jack bought 4 rulers and 5 compasses for $18.92 altogether. If Jacks brother bought 2 rulers and 4 compasses for $14.98, what was the price of each compass?

Price of each compass = $3.68

Price of each ruler = $0.13

Step-by-step explanation:

Let R denote rulers and C denotes compasses

Jack bought 4 rulers and 5 compasses for $18.92

which algebraically translates to

4R + 5C = 18.92 eq. 1

Jack's brother bought 2 rulers and 4 compasses for $14.98

which algebraically translates to

2R + 4C = 14.98 eq. 2

Now we have two equations and two unknowns R and C

Choose any of the above equation and make any of the unknown the subject of the equation.

Choosing eq. 1

4R + 5C = 18.92

4R = 18.92 - 5C

R = (18.92 - 5C) / 4 eq. 3

Now put this value of R into eq. 2

2R + 4C = 14.98

2 ((18.92 - 5C) / 4) + 4C = 14.98

9.46 - 2.5C + 4C = 14.98

1.5C = 5.52

C = 5.52/1.5

C = 3.68

So the price of each compass is $3.68

We can verify whether our answer is right or not. First we have to find the cost of R

Put this value of C into eq. 3

R = (18.92 - 5C) / 4

R = (18.92 - 5*3.68) / 4

R = (18.92 - 18.4) / 4

R = 0.52/4

R = 0.13

So the price of each ruler is $0.13

Now let us verify:

from eq. 1

4R + 5C = 18.92

4 (0.13) + 5 (3.68) = 18.92

0.52 + 18.4 = 18.92

18.92 = 18.92 (hence proved)

from eq. 2

2R + 4C = 14.98

2 (0.13) + 4 (3.68) = 14.98

0.26 + 14.72 = 14.98

14.98 = 14.98 (hence proved)