1. Shop T sold a handphone for $425. This price was 15% lower than the price which shop M sold it for. (a) What was the price of the handphone in Shop M? (b) During  a sale , both shops offered equal percentage discounts on the handphone. Smith bought the handphone from Shop M. He paid $57.75 more than the discounted price in Shop T. What was the percentage discount?

(a)

100% ——- $425 (price in Shop T)

100% – 15% = 85%

85% ——- $425

1% ——- $425/85 = $5

100% ——- $5 x 100 = $500 

(b)

Let the discount be x%.

Shop M ——- $57.75 + discounted price in Shop T.

x% of $500 – x% of $425 = (500x/100) – (425x/100) = $57.75

500x – 425x = 75x = 57.75 x 100 = 5775

 x = 5775/75 = 77

100% – 77% = 23%

Ans : (a) $500; (b) 23%.

2. Both David and Eric had an equal amount of money at first. Every month, David spent $850 and Eric spent $912. After a few months, David was left with $1550 while Eric had 4/5 of the money David had left. How much did Eric have at first?

David :

850 x number of months + 1550

Eric :

(4/5) x $1550 = $1240 

912 x number of months + 1240

912 x number of months + 1240 = 850 x number of months + 1550

(912 – 850) x number of months = 62 x number of months ——- 1550 – 1240 = 310

number of months ——- 310/62 = 5

912 x 5 + 1240 = 5800

Ans : $5800.

can explain qn 1 without using algebra?

discounted percentage x 500 = discounted percentage x 425 + 57.75
discounted percentage ——- 57.75/(500 – 425) = 0.77 = 77%
100% – 77% = 23%