The sum of two numbers is 24. Seven times the smaller number is the same as 5 times the larger number. Find the smaller number
i believe its -4
One number is 6 less than another number. The sum of the numbers is 24. Let x and y be the two numbers.
Which system of equations can be used to find the numbers?
To find the smaller number, let's represent the two numbers as variables. Let's call the smaller number "x" and the larger number "y".
According to the problem, the sum of the two numbers is 24. This can be expressed as:
x + y = 24 ---(Equation 1)
It is also given that seven times the smaller number is equal to five times the larger number. This can be written as:
7x = 5y ---(Equation 2)
Now we have a system of two equations (Equation 1 and Equation 2) with two variables (x and y). We can solve this system of equations to find the values of x and y.
We can start by solving Equation 2 for y:
7x = 5y
y = (7x) / 5
Now, substitute this value of y in Equation 1:
x + y = 24
x + (7x) / 5 = 24
Multiply both sides of the equation by 5 to get rid of the fraction:
5x + 7x = 24 * 5
12x = 120
x = 120 / 12
x = 10
So, the smaller number (x) is 10.