Question 216081
Please help to solve this problem:


The larger of 2 numbers is 20 more than the smaller. 4 times the larger is 70 more than 5 times the smaller, find the number.


thank you
Rick


Step 1.  Let x be the smaller number and let x+20 be the larger number.


Step 2.  Let 4(x+20) be four times the larger.


Step 3.  Let 5x be five times the smaller.


Step 4.  Then {{{4(x+20)= 5x+70}}} since 4 times the larger is 70 more than 5 times the smaller.


Step 5.  The following steps will solve the equation in Step 4.


{{{4(x+20)= 5x+70}}}


{{{4x+80=5x+70}}}


Subtract 4x+70 from both sides of the equation to get x-terms on the right side and numbers on the left side of the equation.


{{{4x+80-4x-70=5x+70-4x-70}}}


{{{10=x}}}  and {{{x+20=30}}}


Check if {{{4(x+20)= 5x+70}}} or {{{4*30=5*10+70}}} which is a true statement.


Step 6. ANSWER.  The numbers are 10 and 32.


I hope the above steps were helpful. 


For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.


And good luck in your studies!


Respectfully,
Dr J