I don't know how to get answer for problem The larger of two numbers is 20 more than the smaller. Four times the larger is 70 more than 5 times the smaller. find the numbers
Let L stand for the larger and S stand for the smaller.
From the second sentence, you know that L = S + 20.
From the second sentence, you know
4L = 5S + 70
Substitute S + 20 for L in the second equation. Solve for S. Put value of S in the first equation to solve for L. Check answers by putting both values in the second equation.
I hope this helps. Thanks for asking.
The larger of two numbers is 3 times the smaller. Their sum
is 8 more than twice the smaller. Find the numbers.
To find the two numbers, we can set up a system of equations based on the given information. Let's assume the smaller number is represented by 'x' and the larger number is represented by 'y'.
Based on the given information, we can write the following equations:
1. "The larger of two numbers is 20 more than the smaller":
y = x + 20
2. "Four times the larger is 70 more than 5 times the smaller":
4y = 5x + 70
Now we have a system of two equations with two variables:
Equation 1: y = x + 20
Equation 2: 4y = 5x + 70
Solving this system of equations will allow us to find the values of x and y.
One way to solve this is to substitute the value of y from equation 1 into equation 2:
4(x + 20) = 5x + 70
Now, distribute 4 to the terms inside the parentheses:
4x + 80 = 5x + 70
Next, bring all the terms involving x to one side of the equation:
4x - 5x = 70 - 80
-x = -10
Now, multiply both sides of the equation by -1 to solve for x:
(-1)(-x) = (-1)(-10)
x = 10
So, the smaller number is 10.
Plugging the value of x into equation 1, we can find the value of y:
y = x + 20
y = 10 + 20
y = 30
Therefore, the larger number is 30.
To summarize, the smaller number is 10 and the larger number is 30.