Question

David scored x marks for his mathematics test, Edwin scored 4/5 of what David scored. Frank scored 38 marks more than Edwin and Gabriel scored 5 fewer marks than Frank.
(a) Express Gabriel's marks in terms of x.
(b) if the average mark of the four boys is 64.5, find Gabriel's marks for the Mathematics test. ​

Answer 1

D=x

E=(4/5)•x

F=E+38

F=(4/5)•x+38

G=F-5

G=(4/5)x+38-5

G=(4/5)x+33. ⟨——answer for A

64.5=[d+e+f+g]/4

64.5=[5x/5+4x/5+4x/5+38+4x/5+33]/4

4•64.5=9x/5+8x/5+71

258=17x/5+71

258-17=17x/5

241=17x/5

5•241=17x

1205/17=x

70.88=x

G=(4/5)x+33

G=(4/5)(70.88)+33

G=89.7 ⟨——answer to part B

Answer 2

Gabriel's marks in terms of x is (G = 4x/5 + 38) and if the average mark of the four boys is 64.5 then Gabriel's marks for the Mathematics test is 89.7.

Given :

• David scored x marks for his mathematics test, Edwin scored 4/5 of what David scored.
• Frank scored 38 marks more than Edwin and Gabriel scored 5 fewer marks than Frank.

Score of David in the mathematics test is given by:

D = x

Score of Edwin in the mathematics test is given by:

$\rm E = \dfrac{4}{5}x$

Score of Frank in the mathematics test is given by:

$\rm F = \dfrac{4}{5}x + 38$

Score of Gabriel in the mathematics test is given by:

G = F - 5    ---- (1)

a) Now, substitute the value of F in the equation (1)

$\rm G = \dfrac{4x}{5}+38-5$

$\rm G = \dfrac{4x}{5}+33$

b) Given that the average mark of the four boys is 64.5 that is:

$\rm \dfrac{G+F+E+D}{4}=64.5$

Now, substitute the values of G, F, E, and D in the above equation. After simplifying the expression:

$258=\dfrac{17x}{5}+17$

Further, simplify the above expression it becomes:

x = 70.88

So, Gabriel's marks for the Mathematics test is:

$\rm G = \dfrac{4\times 70.88}{5}+33$

G = 89.7

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