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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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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    2021-09-22T18:11:00+00:00

    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

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