Question

The weekly allowance Danny and Anton each receive are in the ratio 2 : 1. If Danny gives $8 to Anton, the ratio becomes 2 : 3. Let Anton's allowance be $x, form an equation in term of x and find their allowance respectively.

Answer 1

Jawab:

Before Danny gives $8 to Anton

1. Anton's Allowance = $6
2. Danny's Allowance = $12

After Danny gives $8 to Anton

1. Anton's Allowance = $6 + $8 = $14
2. Danny's Allowance = $12 - $8 = $4

Penjelasan dengan langkah-langkah:

[tex]\frac{Danny's Allowance}{Anton Allowance} = \frac{2}{1}[/tex]

if, Anton's Allowance = $x & Danny's Allowance = $y, so

1. [tex]\frac{y}{x} = \frac{2}{1}[/tex] ; the value of [tex]y = 2x[/tex]
2. If Danny gives $8 to Anton, [tex]\frac{y-8}{x} = \frac{2}{3}[/tex]

 [tex]y=2x[/tex]   ⇒  [tex]\frac{2x-8}{x} = \frac{2}{3}[/tex]  ⇒  [tex]3(2x-8)=2x[/tex]  ⇒  [tex]6x-24=2x[/tex]  ⇒  [tex]6x-2x=24[/tex]

[tex]4x=24[/tex]  ⇒  [tex]x=6[/tex] and [tex]y=2x[/tex] ⇒ [tex]y=12[/tex]

Before Danny gives $8 to Anton

1. Anton's Allowance = $6
2. Danny's Allowance = $12

After Danny gives $8 to Anton

1. Anton's Allowance = $6 + $8 = $14
2. Danny's Allowance = $12 - $8 = $4