question in maths?

Question

please give me the algebraic meaning of this :
the sum of two numbers is 17 and one of them exceeds the other by 10 what are the two numbers
i need this translated into equations and solved using substitution method

Answer 1

you have to substitue each number by a letter to make it easier
let the bigger number = x
let the smaller number = y
the sum is 17 ------------------------------ means x + y = 17
one exceeds other by 10 ( we assumed x is bigger )
-------------------------------------------------means x - y = 10
here you have two simultaneous equations in two variables x , y
allign them vertically
x + y = 17
x - y = 10
--------------- add
2x = 27 divide by 2
x = 13.5
to get y substitue in the upper one
13.5 + y = 17 sub. 13.5
y = 17 - 13.5 = 3.5
then the two numbers are 13.5 , 3.5

check : sum = 3.5 + 13.5 = 17
diff = 13.5 - 3.5 = 10 ok
hope that helps

Answer 2

Follow these steps to solve the problem:

Step 1 : Let the two numbers be (A) and (B).

Step 2 : A+B = 17 ( sum of two numbers is 17)

Step 3 : A-B = 10 (one of them exceeds the other by 10 think of it as A=B+10)

Your two equations: A+B=17
A-B= 10

Answer 3

Let x be the first number and y the other
The sum of two numbers is 17: x + y = 17
One exceeds the other by 10: x = y + 10
x + y = 17
x - y = 10
Add:
2x = 27, x = 27/2
y = x - 10 = 27/2 - 20/2 = 7/2

Answer 4

x + y = 17 (sum of two numbers is 17)
x = y + 10 (one exceeds the other by 10)

replacing x with y + 10
y + 10 + y = 17
2y + 10 = 17
2y = 7
y = 3/2

Answer 5

let the 2 numbers be x and y
x + y = 17
y = x + 10

Answer 6

let the number be x and y. and x is the bigger number...
x+y = 17 ............................(1) eq
x-y = 10...............................(2) eq
solving 2nd eq further , we get x = 10+y.........(3)eq,
putting this value in equation 1, we get
( 10+y) + y = 17
10+2y =17
2y = 7
y = 7/2.
putting this value in eq(3)
we get
x = 7/2 +10
x = 27/2.

Answer 7

a+b=17
a=b+10
a,b=?

b+10+b=17 (you substitute a with b+10)
2b+10=17
2b=17-10
2b=7
b=7/2
b=3.5

a=b+10
a=3.5+10
a=13.5

problem solved: a=13.5 and b=3.5