The sum of 2 numbers is 26. Four times the first number plus twice the second is 70. What are the numbers?
one number --- x
the other ----- 26-x
Now translate the English sentence into Math
" Four times the first number plus twice the second is 70" -----> 4x + 2(26-x) = 70
thnk so mch
To solve this problem, let's assign variables to the unknown numbers. Let's call the first number 'x' and the second number 'y'.
According to the problem, the sum of the two numbers is 26. We can write this information as an equation: x + y = 26 (Equation 1).
The problem also states that four times the first number plus twice the second number is equal to 70. We can write this as the equation: 4x + 2y = 70 (Equation 2).
Now we have a system of two equations (Equations 1 and 2) that we can solve simultaneously to find the values of x and y.
There are different methods to solve this system of equations, such as substitution or elimination. Let's use the elimination method here.
To eliminate one of the variables, we need to multiply both sides of one of the equations by a constant that will make the coefficient of one variable equal in both equations. In this case, we can multiply Equation 1 by 2 and Equation 2 by -1.
2(x + y) = 2(26) ==> 2x + 2y = 52 (Equation 3)
-1(4x + 2y) = -1(70) ==> -4x - 2y = -70 (Equation 4)
Now if we add Equations 3 and 4 together, the y term will cancel out:
(2x + 2y) + (-4x - 2y) = 52 + (-70)
- 2x = -18
Dividing both sides by -2, we get: x = 9.
Now that we have x = 9, we can substitute this value back into Equation 1 to find y:
9 + y = 26
y = 26 - 9
y = 17.
Therefore, the two numbers are 9 and 17.