## 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

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

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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