word problem leading to simultaneous equations - example2

The cost of 2 chairs and 3 tables is $950. If the cost of a dozen of chairs and 5 tables is $2450, find the cost of a chair and a table

Solution

Step1 – assume letters (unknown as follows)

Let the cost of a chair be $g

And the cost of a table be $h

Step2 – derive mathematical statements

From the first sentence, we are told that cost of a 2 chairs and 3 tables is $950

Thus, we derive that

2g + 3h = 950 (and we mark this equation1)

From the second sentence, we are told that cost of 12 chairs and 5 tables is $2,450

Again, we derive that

12g + 5h = 2450 (and we mark this equation2)

The equations are now re-arranged as follows

2g + 3h = 950           …      equ1

12g + 5h = 2450     …      equ2

Step3 – solve using elimination method

Using elimination method, we decide to make the coefficients of g equal in the two equations. To do this, we multiply equation1 by 6 since 2g * 6 will give us 12g

6(2g + 3h = 950) and this becomes

12g + 18h = 5700   (and we call this equ3)

Subtract equ2 from equ3 as follows

12g + 18h  = 5700

12g + 5h  = 2450

0  + 13h  = 3250

Thus,     13h = 3250

h = 3250 ÷ 13

h = 250

Step4 – substitution 250 for h in equ2 as follows

12g + 5h = 2450     …      equ2

12g + 5(250) = 2450

12g + 1250 = 2450

Collect like terms as follows

12g = 2450 - 1250

12g = 1200

g = 1200 ÷ 12

g = 100

Thus, a chair costs $100 while a table costs $250