Replacement

Single Equation + Substitution

First
Kelly spent 1/3 of her money on 5 pens and 11 erasers. The cost of each pen is 3 times the cost of each eraser. She bought some more pens with 3/4 of her remaining money. How many pens did she buy altogether?

(Single Equation)
5 P + 11 E = 1/3 money

(Cost)
Pen : Eraser
= 3u : 1u

(Equivalent Quantity)
3u = 1 Pen = 3 Erasers

(Replacement Quantity)
11 Erasers = 1 Pen / 3 Eraser x 11 Erasers = 11/3 Pens = 3 2/3 Pens

(Replacement)
5 P + 3 2/3 P = 1/3 money
8 2/3 P = 1/3 money
1 money = 8 2/3 x 3 = 26 P

3/4 of remaining money = 3/4 x 2/3 = 1/2 money
1/2 money = 13 P

5 P + 13 P = 18 P altogether

Second
Danny spent 3/8 of his money on 10 identical markers and 10 identical files. He then spent 1/10 of the remainder on 6 pens. 
Each file cost 5 times as much as each marker and each pen cost $2.50 more than a marker.How much did each marker cost?

(Single Equation)
10 M + 10 F = 3/8 money

(Cost)
File : Marker
= 5u : 1u
5u = 1 F = 5 M
10 F = 50 M

10 M + 50 M = 3/8 money
60 M = 3/8 money
6 M = 

1/10 of remainder = 1/10 x 5/8 = 1/16  money
6 P = 1/16 money








3 shirts and 4 dresses cost $180. A dress cost 1 1/2  times as much as a shirt. What is the cost of a dress? 

Units Method

1 1/2 = 3/2

1 Dress = 3u

4 Dresses = 12u

1 Shirt = 2u

3 Shirts = 6u

12u + 6u = 18u

18u = $180

1 Dress = 3u = $30

Inverse Proportion Method

1 Dress : 1 Skirt

= 3u : 2u

6u = 2 Dresses = 3 Skirts

2 Dresses + 4 Dresses = $180

6 Dresses = $180

1 Dress = $30

Madam Halimah bought 7kg of sugar and 10kg of flour for $26.25.
If 3/5kg of sugar costs as much as 3/4kg as flour, find the cost of 1kg of flour.

A) Substitution and Elimination

1) John and Peter have a total mass of 66.6kg. Peter and Yenni have a total mass of 48.6kg. John is thrice as heavy as Yenni.  What is John's mass?