The larger of two numbers is 7 less than twice the smaller number. If the sum of the numbers is 47,
find both numbers.

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.

yes

step-by-step explanation: