Forming Simple Equations (1)

Algebra Level 3

The number which, when subtracted from the terms of ratio a : b a : b makes it equal to c : d c : d , is:

1. 1. a b − c d a b + c d \dfrac{ab-cd}{ab+cd}

2. 2. b c − a d c − d \dfrac{bc-ad}{c-d}

3. 3. a + x b + c \dfrac{a+x}{b+c}

4. 4. None of the above

2 4 3 1

Ethan Mandelez by Ethan Mandelez , 15, Malaysia

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1 solution

Ethan Mandelez
May 5, 2020

Form an equation, you will get:

a − x b − x \frac{a-x}{b-x} = c d \frac{c}{d}

Now you can just cross multiply and solve ^_^

d(a-x) = c(b-x)

ad - dx = bc - cx

cx - dx = bc - ad

x(c-d) = bc - ad

x = b c − a d c − d \frac{bc - ad}{c -d}

Simple, right?

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