The sum of two numbers is 180 and the larger number exceeds four times the smaller number by ten, what are the 2 numbers?

2 Answers
Oct 2, 2015

Answer:

The numbers are #110# and #70#.

Explanation:

Be #x# and #y# the two numbers. We know that

#x+y=180# and that

#x=y+4*10#

If we replace #x# with #y+40# we find

#y+40+y=2y+40=180#

#rarr 2y=180-40=140#
#rarr y=140/2=70#

Then we find

#x=70+40=110#

#rarr x+y=110+70=180#

Oct 2, 2015

Answer:

The numbers are: #34# and #146#

Explanation:

The problem is to find such numbers, that:

  1. Their sum is 180
  2. Larger number exceeds 4 times the smaller by 10.

These conditions lead to folowing system of equations:

#{(x+y=180),(y=4x+10):}#

If we substitute #y# in yje first equation we get:

#x+4x+10=180#
#5x+10=180#
#5x=170#
#x=34#

Now we can substitute #x# in any equation to calculate #y#:

#y=4*34+10#
#y=136+10#
#y=146#

Finally we can write the answer:

#{(x=34),(y=136):}#