There are 2 numbers whose sum is 53. 3 times the smaller number is equal to 19 more than the larger number. Which are the numbers?
4 Answers
hala718 | High School Teacher | (Level 1) Educator Emeritus
assume that the fsmaller number =S and the larger number is=L
then, S+L= 53....... (1)
3 times the smaller number = 19 more than the larger number
==> 3 S = 19 + L ........ (2)
Now, combining equation (1) and (2) we have:
S+L = 53
3S = 19 + L ==> L = 3S -19
substitute in eqution (1),
S + (3S- 19) = 53
4S - 19 = 53
4S = 72 divide by 4
S = 72/4 = 18
and L = 3(18)- 19 = 35
pohnpei397 | College Teacher | (Level 3) Distinguished Educator
The larger number is 35 and the smaller number is 18. Here is how to find this.
Let X be the smaller number and Y be the larger.
x + y = 53
3x = y + 19
Let us solve for y in the first equation.
y = 53 -x
Then let us substitute that for y in the second equation.
3x = 53 - x + 19
3x = -x + 72
4x = 72
x = 18
If x = 18
18 + y = 53
y = 35
Put a=the smaller number and b=the larger number.
Their sum is 53.
a+b=53 (1)
Now we'll write the constraint: 3 times smaller is equal to 19 more than larger.
3a = b+19
3a-b = 19 (2)
If we'll add (1) to (2), we'll have:
a+b+3a-b = 53+19
4a = 72
a = 18
If we'll substitute the value for a in equation (1), we'll get:
a+b = 53
18+b = 53
b = 53-18
b = 35
neela | High School Teacher | (Level 3) Valedictorian
Let x and y be the 2 numbers . So by data x+y =53.....(1)
If x is smaller number, the 3x = y+19....(2) From (2) we get:
3x-y = 19....(3)
x+y = 53...(1)
(1)+(2) gives: 4x = 19+53 = 72.. Or x= 72/4 = 18 is the smaller number and y= 53-x = 53 -18 =35.