Answer:
larger number=29;smaller number=18
Step-by-step explanation:
let assume the two numbers are X and Y
where X is the larger number and Y is the smaller number.
From the question the larger number is 7 less than twice the smaller number. in mathematical terms this can be denoted as;
X=2Y - 7→→→→→→ equation 1
Also it was stated in the question that the sum of the two numbers is 47 which can be denoted as;
X + Y = 47→→→→→→ equation 2
Now from equation 1, X is mathematically expressed as 2Y - 7. Having known this we substitute X as 2Y - 7 into equation 2 then we have 2Y - 7 + Y = 47.
collecting like terms we have
2Y + Y = 47 + 7
solving arithmetically we have;
3Y = 54
divide both sides by 3 we have;
Y = 18.
Now if you recall from equation 1;
X = 2Y - 7;
since we now know Y as 18 we substitute Y as 18 in equation one then we have;
X = 2(18) - 7;
X =36 - 7
X = 29.
