Chap 4 (Recap 1) Let's TALK Algebra before the test ^.^

Jane has x 5¢ coins and y 10¢ coins.

(a) If x = 10 and y = 20, what would be the total value of the coins?
(b) If y = 2x, explain what does this statement mean?
(c) If the total value of coins was \$1.50, write 2 other possible combination of coins in terms of x and y.

1. a) \$0.50+\$2=\$2.50

b) y is equivalent to x+x

c) 1. x=9 y=10.5
2. x=8 y=11

2. a)10(\$0.05)+20(\$0.10)=\$0.50+\$2
=\$2.50

b) It means that y is equal to 2 of x.

c) i)x=20 and y=5
ii)x=14 and y=8

3. a) 10×\$0.05+20×\$0.10=\$2.50
b) y=x+x
c) x=10
y=10

4. (a)10(5cents) + 20(10cents)
= 50cents + 200cents
= 250cents
=\$2.50
(b) y = x + x or y is two times of x.
(c)x = 2, y = 14
x = 4, y = 13

JJ(:

5. 5÷100=0.05
20÷100 = 0.20

a) x x 0.05=0.05x
y x 0.20=0.20y
0.20y + 0.05x= \$(0.20y+0.05x)( ANS)

b)y=2x
y = 2 x x

ci) x=\$0.20
y=\$0.20
ii)x= \$ 0.25
y=\$0.50

6. The answers to the 3 parts are as follows:

(a)
Total value of coins
= 10 times 5¢ + 20 times 10¢
= 50¢ + 200¢
= 250¢ or \$2.50

Alternatively, we can convert the value of each coin to \$ first and work from there (which most of you did)

(b)
y = 2x means there are 2 times as many 5¢ coins as the 10¢ coins
(in other words, for every 10¢ coin, there are 2 5¢ coins there)

Note: When the question asked what the expression means, we normally refer to the context (here, it's coins), to explain the meaning of the equation.

(c) There are many combinations, however, we have to bear in mind that x and y refers to the NUMBER of coins. Therefore, x and y must be whole numbers. We cannot 'cut' a coin into 2 parts, isn't it?

PS:
Shamus will have to relook at the 1st combination... is it possible?
Jonathan will need to help us understand what do x and y represent in your answers?

7. Let's look at Part (c)...

Here are some questions to ponder... let's make reference to what's contributed so far,

1. Do you think there's a systematic way to find the answer?

2. Do you think there are UNLIMITED number of possible solutions to this part?

3. How would you find out ALL (if possible) the possible answers?

4. Is there any ICT tool that you think could help you to generate ALL (if possible) the possible asnwers?