Given that 2a : 5c = 6 : 25 and [math]4b : 7c = 20 : 21[/math],
Show that (a+b) : (b+c) = 17 : 20
Level
GCSE
Exam Board
Edexcel
- Najma asked 1 week ago
- last edited 1 week ago
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We are given:
\[ 2a:5c=6:25 \]
\[ 4b:7c=20:21 \]
We need to show that
\[ (a+b):(b+c)=17:20 \]
Step 1: Find the ratio of a:c
From 2a:5c=6:25,
\[ \frac{2a}{5c}=\frac{6}{25} \]
Cross-multiply:
\[ 50a=30c \]
Divide both sides by 10:
\[ 5a=3c \]
Therefore,
\[ \boxed{a:c=3:5} \]
Step 2: Find the ratio of b:c
From 4b:7c=20:21,
\[ \frac{4b}{7c}=\frac{20}{21} \]
Cross-multiply:
\[ 84b=140c \]
Divide both sides by 28:
\[ 3b=5c \]
Therefore,
\[ \boxed{b:c=5:3} \]
Step 3: Make the value of c the same in both ratios
We have:
\[ a:c=3:5 \]
\[ b:c=5:3 \]
The lowest common multiple of 5 and 3 is 15.
Multiply the first ratio by 3:
\[ a:c=9:15 \]
Multiply the second ratio by 5:
\[ b:c=25:15 \]
Therefore,
\[ \boxed{a:b:c=9:25:15} \]
Step 4: Work out (a+b):(b+c)
Substitute the values:
\[ (a+b):(b+c) \]
\[ =(9+25):(25+15) \]
\[ =34:40 \]
Divide both parts by 2:
\[ \boxed{17:20} \]
Hence, we have shown that
\[ \boxed{(a+b):(b+c)=17:20} \]
- Najma answered 1 week ago
- last edited 1 week ago
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