Question 1191337
Hi
If Bob  had twice as many nickels and half as many quarters, he would have 60c less. Suppose he now has 16 nickels and quarters. How many of each coin does he have.

Thanks 
<pre>Let number of nickels be N
Then number of quarters = 16 - N
Amount of money: .05N + .25(16 - N) = - .2N + 4
If there were twice as many nickels, then number of nickels would be 2N

It there were twice as many nickels, then value of the nickels would be .05(2N) = .1N
If there were half as many quarters, then number of quarters would be {{{matrix(1,3, (16 - N)/2, or, 8 - N/2)}}}
If there were half as many quarters, then the value of the quarters would be {{{matrix(1,3, .25(8 - N/2), "=", 2 - .25N/2)}}}

Since hypothetical scenario yields .60 less, we then get: {{{matrix(3,3, .1N + 2 - .25N/2, "=", - .2N + 4 - .6, .1N - .25N/2 + .2N, "=", 3.4 - 2, .3N - .25N/2, "=", 1.4)}}}
                                                               .6N - .25N = 2.8 ------ Multiplying by LCD, 2
                                                                     .35N = 2.8
                                            <font color = red><font size  = 4><b>Number of nickels</font></font></b>, or {{{highlight_green(matrix(1,7, highlight(N), "=", 2.8/.35, "=", 280/35, "=", highlight(8)))}}}

                                            Obviously, <font color = blue><font size  = 4><b>number of quarters: 16 - 8 = 8</font></font></b></pre>