Aboxcontains8red,5green,2brown,3purple,1blue, and 6 yellow candles.

Question

a) Write each ratio.
i) red:purple ii) green:blue
iii) purple:green iv) brown and yellow:total candles
b) What if 3 red, 2 green, and 4 yellow candles were burned?
Write the new ratios for part a.

Answer 1

Let's start by calculating the total number of candles in the box.

Total candles = red + green + brown + purple + blue + yellow
Total candles = 8 + 5 + 2 + 3 + 1 + 6 = 25 candles

Now, we can find the ratios for part (a):

Part (a):

i) Red: Purple
Red = 8, Purple = 3
Ratio = 8:3

ii) Green: Blue
Green = 5, Blue = 1
Ratio = 5:1

iii) Purple: Green
Purple = 3, Green = 5
Ratio = 3:5

iv) Brown and Yellow: Total Candles
Brown = 2, Yellow = 6
Total candles = 25
Ratio = (2 + 6):25 = 8:25

Part (b):

Now, let's see what happens if 3 red, 2 green, and 4 yellow candles are burned.

New counts after burning:

• Red = 8 - 3 = 5
• Green = 5 - 2 = 3
• Brown = 2 (not affected)
• Purple = 3 (not affected)
• Blue = 1 (not affected)
• Yellow = 6 - 4 = 2

Now let's find the new total:

New Total Candles = 5 + 3 + 2 + 3 + 1 + 2 = 16 candles

Now, we can find the new ratios for part (b):

i) Red: Purple
Red = 5, Purple = 3
Ratio = 5:3

ii) Green: Blue
Green = 3, Blue = 1
Ratio = 3:1

iii) Purple: Green
Purple = 3, Green = 3
Ratio = 3:3 = 1:1

iv) Brown and Yellow: Total Candles
Brown = 2, Yellow = 2
Total candles = 16
Ratio = (2 + 2):16 = 4:16 = 1:4

Summary:

Part (a) Ratios:

1. Red:Purple = 8:3
2. Green:Blue = 5:1
3. Purple:Green = 3:5
4. Brown and Yellow:Total Candles = 8:25

Part (b) New Ratios:

1. Red:Purple = 5:3
2. Green:Blue = 3:1
3. Purple:Green = 1:1
4. Brown and Yellow:Total Candles = 1:4