Question

The sum of two numbers is 18. 5 times the first number subtracted from 4/7 of the second number is 14. Find the number.

Answer 1

To solve this problem, set up and solve a system of equations. The two numbers are -46 and 64.

Step-by-step explanation:

To solve this problem, we can set up a system of equations. Let's use variables to represent the two numbers. Let's call the first number x and the second number y. From the given information, we can write two equations:

Equation 1: x + y = 18 (since the sum of the two numbers is 18)

Equation 2: (4/7)y - 5x = 14 (since 5 times the first number subtracted from 4/7 of the second number is 14)

Now, we can solve this system of equations to find the values of x and y. We can start by solving Equation 1 for x: x = 18 - y. Then, we substitute this expression for x into Equation 2:

(4/7)y - 5(18 - y) = 14. Simplifying this equation gives us:

(4/7)y - 90 + 5y = 14

Using algebraic techniques, we can solve for y:

(4/7)y + 5y = 14 + 90

(4/7)y + (7/7)y = 104

(11/7)y = 104

y = (104 * 7) / 11

y = 64

Now that we know y = 64, we can substitute this value back into Equation 1 to find x:

x + 64 = 18

x = 18 - 64

x = -46

So, the two numbers are -46 and 64.

Answer 2

The sum of two numbers is 18.

5 times the first number subtracted from 4/7 of the second number is 14.

First number --> x

Second number --> y

so

x + y = 18 --> x = 18-y

5x - (4/7)y = 14

so

5 (18-y) - (4/7)y = 14

90 - 5y - 4/7 y = 14

-5.57 y = 14-90

y = 13.64

so

x = 18 - 13.64

x = 4.36