SOLUTION: The difference between two positive numbers is 4 .If twice the number is added to three times the smaller ,the sum is 53.Which are the steps to the solution?

Question 175061: The difference between two positive numbers is 4 .If twice the number is added to three times the smaller ,the sum is 53.Which are the steps to the solution?
Answer by Mathtut(3670) (Show Source): You can put this solution on YOUR website!
first read the problem carefully:
next, turn this from a word problem to an equation or system of equations
:
we have 2 unknown numbers lets call them a and b
the difference(we know subtraction is involved here) between 2 postive numbers(a and b) equals 4...so a-b=4. In this next sentence they are distinguishing these numbers as smaller and larger. From the first equation we know in our case, that a is the larger and b the smaller. twice(2a)is added to(+3b) equals 53. so we have 2 equations
:
a-b=4.....eq 1
2a+3b=53..eq 2
:
now lets solve. Re write eq 1 to a=4+b and take a's value of 4+b and plug it into eq 2
:
2(4+b)+3b=53
:
8+2b+3b=53
:
5b=45
:

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