The two numbers are 6 and 10 which sums to 16.
Step-by-step explanation:
It is given that, the sum of two numbers is 16.
Let,
Therefore, x+y = 16 forms the first equation.
It is given that, the total of three times the smaller and twice the larger is 42.
This means that,
Three times the smaller ⇒ 3x.
Twice the larger ⇒ 2y.
The total of three times the smaller and twice the larger is 42 can be represented as (3x+2y) = 42 which forms the second equation.
The system of equations are :
x+y = 16 --------(1)
3x+2y = 42 -------(2)
Multiply eq (1) by 2, and subtract eq (2) from eq (1),
2x+2y = 32
-(3x+2y = 42)
-x = - 10
Therefore, the value of x is 10.
To find the number y :
Substitute x=10 in eq (1),
10+y = 16
y = 6.
The other number is 6.
two numbers are 10 and 6 .
Step-by-step explanation:
Here we have , The sum of two numbers is 16. The total of three times the smaller and twice the larger is 42 . We need to find the two numbers . Let's fins out:
Let two numbers be x & y so ,
The sum of two numbers is 16
With this info we have following linear equation:
⇒ [tex]x+y=16[/tex]
The total of three times the smaller and twice the larger is 42
With this info we have following linear equation:
⇒ [tex]3x+2y=42[/tex]
Let's solve these
⇒ [tex]3x+2y=42[/tex]
⇒ [tex]x+2(x+y)=42[/tex] { [tex]x+y=16[/tex] }
⇒ [tex]x+2(16)=42[/tex]
⇒ [tex]x=10[/tex]
Putting [tex]x=10[/tex] in [tex]x+y=16[/tex] we get:
⇒ [tex]10+y=16[/tex]
⇒ [tex]y=6[/tex]
Therefore, two numbers are 10 and 6 .
