Question 1208132
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Hi
Mr Jones has some notes. 1/5 of them are 2 dollar notes. 3/8 of the remainder are 10 dollar notes. The remaining notes are 5 dollar notes. The total sum he has $295 . How many 10 dollar notes does he have.

Let number of notes be N
Then number of $2 notes = {{{matrix(1,5, 1/5, of, N, "=", N/5)}}}, and remaining notes = {{{matrix(1,8, (1 - 1/5), of, N, "=", (4/5),"N,", or, 4N/5)}}}
Also, number of $10 notes = {{{matrix(1,9, 3/8, of, 4N/5, "=", (3/8)(4N/5), "=", (3/2cross(8))(cross(4)N/5), "=", 3N/10)}}}
Remaining notes (number of $5 notes) = {{{matrix(1,9, (1 - 3/8), of, 4N/5, "=", (5/8)(4N/5), "=", (cross(5)/2cross(8))(cross(4)N/cross(5)), "=", N/2)}}}
                Amount in $2 notes: {{{matrix(1,3, 2(N/5), "=", 2N/5)}}}
             Amount in $10 notes: {{{matrix(1,3, 10(3N/10), "=", 3N)}}}
                Amount in $5 notes: {{{matrix(1,3, 5(N/2), "=", 5N/2)}}}
                              Total amount: $295

                    We now get: {{{matrix(1,3, 2N/5 + 3N + 5N/2, "=", 295)}}}
                             4N + 30N + 25N = 2,950 ----- Multiplying by LCD, 10
                                        59N = 2,950
                     Number of notes, or {{{matrix(1,5, N, "=", "2,950"/59, "=", 50)}}}
                   Number of $10 notes: {{{highlight_green(matrix(1,9, 3N/10, "=", 3(50)/10, "=", 3(5cross(50))/cross(10), "=", 3(5), "=", highlight(15)))}}}</pre>