The sum of two counting numbers is 243. Half of one number is four times the other
number. What are the numbers?
121.1+122.2=243.2
what's all this 121, 122 junk? Guessing?
If the numbers are x and y, just write down what they told you:
x+y = 243
x/2 = 4y
so, x=8y and we have
8y+y=243
9y=243
y=27
so, x=216
x+y=243 1/2x=4y x=8y 8y+y=243 9y=243 y=27 x+27=243 x=216
To find the two numbers, let's set up equations based on the information given.
Let's say the first number is represented by x, and the second number is represented by y.
We are given two pieces of information:
1. The sum of the two numbers is 243: x + y = 243.
2. Half of one number (let's say x/2) is four times the other number (y): x/2 = 4y.
Now, we have a system of two equations. To find the values of x and y, we can solve these two equations simultaneously.
First, let's isolate x in the second equation by multiplying both sides by 2:
x = 8y.
Now, substitute this value of x in the first equation:
8y + y = 243.
Combining like terms:
9y = 243.
Divide both sides by 9:
y = 27.
Now, substitute this value of y back into the second equation to find x:
x/2 = 4(27).
x/2 = 108.
Multiply both sides by 2:
x = 216.
So, the two numbers are 216 and 27.