Question 1169761
Some children share an amount of money equally and each of them gets $20. If the number of children sharing the same amount of money is reduced by 5, each child will get $40. Find the amount of money. 
<pre>Let amount of money be A
Then number of children = {{{A/20 }}}
Reducing number of children by 5 makes the new number {{{A/20 - 5}}}
So, amount each child would get = {{{A/(A/20 - 5)}}}, and so, we get: {{{matrix(1,3, A/(A/20 - 5), "=", 40)}}}
              
                                                            {{{matrix(1,3, A/((A - 100)/20), "=", 40)}}}                    
                                                            
                                                            {{{matrix(1,3, A * (20/(A - 100)), "=", 40)}}}</pre><pre>
                                                            {{{matrix(1,3, 20A/(A - 100), "=", 40)}}}
                                                            
                                                            {{{matrix(1,3, A/(A - 100), "=", 2)}}} ----- Factoring out LCD, 20, in numerator
                                                           
                                                            A = 2(A - 100) ---- Cross-multiplying
                                                            A = 2A - 200
                                                            A - 2A = - 200
                                                          - A = - 200 
                                       Amount of money, or {{{highlight_green(matrix(1,5, A, "=", (- 200)/(- 1), "=", "$200"))}}}</pre>