Question

In an examination, Chukwu score 20 more in Mathematics than in French and his Social Studies was half his Mathematics score. His total score was greater than 110. Find the possible score in Mathematics.​

Answer 1

Mathematics score ≥ 52

Explanation:

Inequalities:

Let the score in French = x

Score in Mathematics = 20 more than French

= 20 + x

Score in social studies = half of mathematics score

`= (1)/(2)*(20 +x)`

`= (1)/(2)*20 + (1)/(2)*x \ \ \ {\text{\bf [Distributive property]}}\\\\= 10 + (1)/(2)x`

Total score > 110

`x + x + 20 + 10 + (1)/(2)x > 110\\\\\ \ \ \ \ \ \ \ \ 30 + 2x + (1)/(2)x > 110\\\\`

`30 + (4x+x)/(2) > 110`

`30 + (5x)/(2) > 110`

Subtract 30 from both sides,

`(5x)/(2) > 110 - 30\\\\ (5x)/(2) > 80`

Multiply the entire equation by 2,

5x > 80*2

5x > 160

Divide both sides by 5,

x> 160 ÷5

x > 32

Mathematics is 20 more than x.

Mathematics marks will be greater than or equal to 52.

Mathematics score ≥ 52