(a) Wayne's savings before he spent $28 is $30.
(b) Stef's savings after she spent $28 is $8.
Solution:
Ratio of Wayne's savings to Stef's savings = 5 : 6
Let x be the common amount they have.
After spending $28 each, the ratio becomes 1 : 4.
5x – 28 : 6x – 28 = 1 : 4
This can be written in a fraction form.
[tex]$\Rightarrow\frac{5x-28}{6x-28}=\frac{1}{4}[/tex]
Do cross multiplication.
[tex]$\Rightarrow 4(5x-28)}=1({6x-28})[/tex]
[tex]$\Rightarrow 20x-112=6x-28[/tex]
Arrange like term one side.
[tex]$\Rightarrow 20x-6x=112-28[/tex]
[tex]$\Rightarrow 14x=84[/tex]
⇒ x = 6
(a) Wayne's savings before he spent $28 = 5x = 5(6) = $30
(b) To find stef's savings after spent $28:
Stef's savings before she spent $28 = 6x = 6(6) = $36
Stef's savings after she spent $28 = $36 – $28 = $8
Hence Wayne's savings before he spent $28 is $30
Stef's savings after she spent $28 is $8.
