http://openstudy.com/groups/mathematics#/groups/mathematics/updates/4e9d9bc20b8b81e687fec11b
willyg123 Neophyte
find four consecutive multiples of 5 such that 6 times the first is 40 greater than 2 times the sum of the second and
the fourth
Reset the Mathematica line counter.
In[6]:=
$Line = 0;
Let x be the largest of four consecutive integers. The following is a list, n, where each of the integers have been
multiplied by 5.
In[1]:=
Out[1]=
n = 5 * 8x - 3, x - 2, x - 1, x<  Expand
8- 15 + 5 x, - 10 + 5 x, - 5 + 5 x, 5 x<
n[[1]] , n[[2]] and n[[4]] are references to the first, second and forth expressions from list n. Mathematica makes the
substitutions, performs the indicated operations on the list elements and simplifies the resulting equation.
“6 times the first is 40 greater than 2 times the sum of the second and the fourth”
In[2]:=
Out[2]=
6 n@@1DD Š 40 + 2 Hn@@2DD + n@@4DDL  Expand
- 90 + 30 x Š 20 + 20 x
Solve the above equation for x.
In[3]:=
Out[3]=
Solve@%, xD
88x ® 11<<
Replace x with 11 in each list element of n and evaluate the result.
In[4]:=
Out[4]=
n . %
8840, 45, 50, 55<<
Verify the solution.
“6 times the first is 40 greater than 2 times the sum of the second and the fourth”
In[5]:=
Out[5]=
86 ´ 40, 40 + 2 H45 + 55L<
8240, 240<