What we need to do is write down the information given to us in the question in terms of equations and then solve them to get the answer. Let's call Lisa's height #L#, Ian's height #h#, and Jim's height #J#. The first statement, "Lisa is 10 centimeters taller than her friend Ian", gives us:
#L= h+10#
The next statement "Ian is 14 centimeters taller than Jim" gives:
#h=J+14#
The following statement "Every month, their heights increase by 2 centimeters. In 7 months..." means that each height has increased by #2cm//month *7 months = 14 cm#, so we must add that to each height in the next statement: "the sum of Ian's and Jim's heights will be 160 centimeters more than Lisa's height":
#(h+14)+(J+14)=(L+14)+160#
where #h#, #J#, and #L# are the initial heights 7 months previously. Finally, we are asked for Ian's height today (not 7 months from now). We can use our first equation to substitute in for #L# in the previous equation:
#(h+14)+(J+14)=(h+10+14)+160#
#(h+14)+(J+14)=h+184#
Then we can use the second equation, solving for #J#:
#J=h-14#
to substitute into the previous equation:
#(h+14)+(h-14+14)=h+184#
#2h + 14 = h + 184#
#h = 170 cm#
