Units & Parts Concept (Change by a Ratio)

Set 1 (Before)
Set 2 (Change)
Amount (2 Sides)

First
James had $2900 and Rose had $1000 at first. After James had bought a laptop that cost twice as much as the laptop Rose bought, James has 5 times as much money left as Rose. How much did Rose's laptop cost?

(Before)
James : Rose
= $2900 : $1000

(Change)
James : Rose
= 2u : 1u

(After)
James : Rose
= 5p : 1p

(James)
$2900 - 2u = 5p

(Rose)
$1000 - 1u = 1p
$5000 - 5u = 5p

5000 - 2900 -5u -(-2u) = 0
2100 - 3u = 0
3u = 2100
Cost of Rose's Laptop = 1u = $700

Second
Carl had $400 and Ester had $120 at first. The book Carl bought cost $30 more than twice the book Ester bought. Carl now has four times as much money left as Esther has left. How much did Carl pay for his book?


(Before)
Carl : Esther
= $400 : $120

(Change)
Carl : Esther
= (2u + $30) : 1u

(After)
Carl : Esther
= 4p : 1p

(Carl)
400 - 2u - 30 = 4p
370 - 2u = 4p

(Esther)
120 - 1u = 1p
480 - 4u = 4p

480 - 370 -4u - (-2u) = 0
110 - 2u = 0
2u = 110

Amount Carl Paid = 2u + $30 = 110 + 30 = $140

Third