• Problem:
Three numbers are in the ratio 1:2:3. Find the largest number if the sum is 96.
• Solution:
✓We can say that the simplest form of the three numbers are 1, 2 and 3. Therefore the numbers are x, 2x and 3x in which x is the common factor.
- Equate the the sum of the numbers to 96.
[tex] \tt x + 2x + 3x = 96 [/tex]
[tex] \tt 6x = 96[/tex]
[tex] \tt x = 96 \div 6[/tex]
[tex] \tt x = 16[/tex]
✓The value of x is 16. That's the common factor. To get the values of the numbers in the given ratio, we should substitute the calculated x to the expressions.
[tex] \tt x = \boxed{\tt 16}\\ \tt 2x = 2(16) = \boxed{\tt32}\\ \tt 3x = 3(16) = \boxed{\tt 48}[/tex]
✓Therefore, the numbers are 16, 32 and 48.
• To check:
[tex] \: \: \: \tt x + 2x + 3x = 96 \\ \tt 16 + 32 + 48 = 96 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt 96 = 96[/tex]
• Answer:
✓The largest number is 48.
