The difference between two numbers is 121. Seven times the smaller is equal to 5 more than the larger. What are the numbers?

x(the bigger number) = 142

y(the smaller number) = 21

Step-by-step explanation:

set up the problem

x - y =121

(we know that y is the smaller number because the answer is not negative, therefore the second number has to be smaller.)

7y = x +5

solve for x

x = 7y - 5

insert the new value of x into the equation

7y - 5 - y = 121

solve for y

6y - 5 = 121

6y = 126

y = 21

substitute the new value of y into the original equation

x - 21 = 121

solve for x

x = 142

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