The difference between two numbers is 31.If 5 is added to the smaller number,the result is equal to half of the larger number.What is the sum of the two numbers?.....(this involves linear equations)...
2006-07-13 22:17:45 · 15 answers · asked by cUrIoSiTy 3 in Science & Mathematics ➔ Mathematics
im on summer break, i dont do math sorry
2006-07-13 22:20:58 · answer #1 · answered by Anonymous · 0⤊ 1⤋
Let the larger number be X and the smaller number be Y
The difference between two numbers is 31,
X - Y = 31 ... (1)
If 5 is added to the smaller number,the result is equal to half of the larger number
(5 + Y) = 1/2 X ... (2)
Multiply both sides of the equation (2) by 2,
2 (5 + Y) = X ... (3)
Substitute (3) into (1)
2 (5 + Y) - Y = 31
10 + 2Y - Y = 31
Y = 31 - 10
Y = 21 ... (4)
Substitute (4) into (1),
X - 21 = 31
X = 52
The sum of the two numbers is,
X + Y = 52 + 21
Answer = 73
2006-07-14 10:35:00 · answer #2 · answered by ideaquest 7 · 0⤊ 0⤋
Assume the larger number is a, and the smaller is b.
a-b=31 (The difference between two numbers is 31)
b+5=1/2a (If you add 5 to the smaller number, the result is equal to one half of the larger number)
a+5=31+a/2 This is adding the two above equations together to remove the b
a/2=26
a=52 (solving for a)
b=52-31=21 (solving for b)
a=52
b=21
a+b=73 (solving for the sum)
2006-07-14 05:21:53 · answer #3 · answered by Eulercrosser 4 · 0⤊ 0⤋
Rewrite the problem in linear equations:
The difference between two numbers is 31.
Decide that,
x is the larger number
y is the smaller number
x - y = 31
If 5 is added to the smaller number,the result is equal to half of the larger number.
y + 5 = (1/2)x
Use the two equations to solve for x and y
y + 5 = (1/2)x ----> x = 2y + 10
x - y = 31 ------> (2y + 10) - y = 31 -----> y = 21
x - (21) = 31
x = 52
What is the sum of the two numbers?
x + y = 21 + 52 = 73
2006-07-14 23:51:00 · answer #4 · answered by Anonymous · 0⤊ 0⤋
Hi!!
Let x = the smaller number = 21
Let x+31 = the larger number = 52
x + 5 = ( x + 31 ) / 2
2x + 10 = x + 31
2x - x = 31 - 10
x = 21
The sum of the two numbers = 21 + 52 = 73
huray!!
might be wrong.. check it again =)
Peace*
2006-07-14 05:29:55 · answer #5 · answered by Tara R 2 · 0⤊ 0⤋
a-b=31 therefore a=b+31
a must be the larger number and b the smaller number to have a positive answer (i.e 31).
so b +5 = 1/2 a
so substitute a in the second equation :
b + 5 = 1/2 a
b + 5 = 1/2 (b+31)
2(b+5)= b +31
2b +10 = b + 31
2b -b = 31-10
b=21
sustitute value of b in the first equation
a-21=31
a=52
so sum of the two number is a+b
52+21=73
the answer is 73
2006-07-14 07:40:44 · answer #6 · answered by pheonix 2 · 0⤊ 0⤋
a-b=31 (The difference between two numbers is 31)
b+5=1/2a
a+5=31+a/2 This is adding the two above equations together to remove the b
a/2=26
a=52 (solving for a)
b=52-31=21 (solving for b)
a=52
b=21
a+b=73 (solving for the sum
2006-07-14 06:25:26 · answer #7 · answered by Anonymous · 0⤊ 0⤋
suppose a the bigger number and b the smaller number
a-b=31
a-(5+b)=(1/)a
a-b=31; a=31+b;
substitute the value of a in the eqn a-(5+b)= (1/2)a
:. (31+b)-(5+b)=(1/2)(31+b)
31-5=1/2(31+b); 26=1/2(31+b)
26*2=31+b; 52=31+b
52-31=b
21=b; a=52
do the next
2006-07-14 06:39:17 · answer #8 · answered by corrona 3 · 0⤊ 0⤋
Let y be the larger no. and x be the smaller no.....
Given:
y-x=31 ---------- (1)
x+5=y/2 ---------- (2)
=> y=2x+10 --------- (3)
Substituting (3) in (1)
2x+10-x=31
=> x=21 -------------(4)
Substituting (4) in (3)
y=52
Sum : x+ y= 21 + 52 = 73
Answer: 73!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
2006-07-14 05:27:45 · answer #9 · answered by sunil 3 · 0⤊ 0⤋
52 and 21
2006-07-14 05:57:36 · answer #10 · answered by love_miel 2 · 0⤊ 0⤋
two added together = 73. smaller number = 21, other 52
2006-07-14 05:23:38 · answer #11 · answered by Twai 2 · 0⤊ 0⤋