Answer:
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)
