Question

Thomas, Janaid and Sara received a total of £75 .Thomas received £8 less than Sara but £5 more than Janaid.How much did they each receive

Answer 1

Write a system of equation based on the problem
Make an algebraic expression for "Thomas, Janaid, Sara received a total of £75"
t + j + s = 75 (first equation)
Make an algebraic expression for "Thomas received £8 less than Sara"
t = s - 8 (second equation)
Make an algebraic expression for "Thomas received £5 more than Janaid"
t = j + 5 (third equation)

Solve the equation system
From the second equation, we need to find the value of s in term of t
t = s - 8
t + 8 = s (fourth equation)

From the third equation, we need to find the value of j in term of t
t = j + 5
t - 5 = j (fifth equation)

Substitute the fourth and fifth equation to the first equation to find the value of t
t + j + s = 75
t + (t - 5) + (t + 8) = 75
3t + 3 = 75
3t = 75 - 3
3t = 72
  t = 72/3
  t = 24
Thomas received £24

Substitute the value of t to the fourth equation to find the value of s
s = t + 8
s = 24 + 8
s = 32
Sara received £32

Substitute the value of t to the fifth equation to find the value of j
j = t - 5
j = 24 - 5
j = 19
Janaid received £19