Answer:
8 and 13
Step-by-step explanation:
Given
Let both numbers be a and b where a > b
So:
[tex]a- b =5[/tex] --- Their difference
[tex]7b + 4a = 108[/tex] --- 7 of smaller and 4 of bigger
Required
Find both numbers
[tex]a- b =5[/tex] --- (1)
[tex]7b + 4a = 102[/tex] --- (2)
Make a the subject in (1)
[tex]a = b + 5[/tex]
Substitute b + 5 for (a) in (2)
[tex]7b + 4(b + 5) = 108[/tex]
Open bracket
[tex]7b + 4b + 20 = 108[/tex]
Collect like terms
[tex]7b + 4b = 108 - 20[/tex]
[tex]11b = 88[/tex]
Divide both sides by 11
[tex]b = \frac{88}{11}[/tex]
[tex]b = 8[/tex]
Substitute 8 for b in [tex]a = b + 5[/tex]
[tex]a = 8 + 5[/tex]
[tex]a = 13[/tex]
Hence the two numbers are 8 and 13
