Question 811694
Two number a & b
Write an equation for each statement
:
The sum of two numbers is 145.
a + b = 145, (a is the larger number)
a = (145-b)
:
 When the smaller number is decreased by two and the larger number is increased by 1,
 their ratio will be 2:7.
{{{((b-2))/((a+1))}}} = {{{2/7}}}
Cross multiply
7(b-2) = 2(a+1)
7b - 14 = 2a + 2
7b = 2a + 2 + 14
7b = 2a + 16
Replace a with (145-b)
7b = 2(145-b) + 16
7b = 290 - 2b + 16
7b + 2b = 306
9b = 306
b = 306/9
b = 34
then
a = 145 - 34
a = 111
:
:
See if that works out
{{{((34-2))/((111+1))}}} = 
{{{32/112}}} reduces to {{{2/7}}}



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