The sum of two numbers is eight. Four less than five times the smaller is equal to the larger.
smaller ---- x
larger --- 8-x
just translate:
"Four less than five times the smaller is equal to the larger"
----> 5x - 4 = 8-x
take over
since their sum is only 8, it would have been quite easy to do this by simple trial-and-error
1 + 7
2 + 6
3 + 5
4 + 4
Which of those pair of numbers meets the criteria?
Why did the number go to circus training? Because it wanted to be in the sum-mer show! Now, let's solve this puzzle together. Let's call the smaller number "x" and the larger number "y." According to the information given, we have two equations:
Equation 1: x + y = 8
Equation 2: 5x - 4 = y
Now, we can substitute Equation 2 into Equation 1:
x + (5x - 4) = 8
Simplifying:
6x - 4 = 8
6x = 8 + 4
6x = 12
x = 12/6
x = 2
We have found the value of the smaller number, which is 2. Now, let's substitute this value back into Equation 1 to find the larger number:
2 + y = 8
y = 8 - 2
y = 6
So, the smaller number is 2 and the larger number is 6.
Let's solve this step-by-step. Let's call the smaller number 'x' and the larger number 'y'.
1. The sum of two numbers is eight.
- x + y = 8
2. Four less than five times the smaller is equal to the larger.
- 5x - 4 = y
Now, we have a system of two equations:
1. x + y = 8
2. 5x - 4 = y
To solve this system of equations, we can use substitution or elimination method.
Let's use substitution method:
1. Rearrange the first equation to solve for x:
x = 8 - y
2. Substitute the value of x in the second equation:
5(8 - y) - 4 = y
Simplify the equation:
40 - 5y - 4 = y
36 - 4y = y
Combine like terms:
36 = 5y
Divide both sides by 5:
y = 36/5
y = 7.2
Substitute the value of y back into one of the original equations to find x:
x + 7.2 = 8
x = 0.8
Therefore, the smaller number 'x' is 0.8 and the larger number 'y' is 7.2.
To solve this problem, let's assign variables to the two unknown numbers. Let's say the smaller number is 'x' and the larger number is 'y'.
We are given two pieces of information. First, the sum of the two numbers is eight: x + y = 8. And second, four less than five times the smaller number is equal to the larger number: 5x - 4 = y.
Now we can solve this system of equations by substitution or elimination method.
Let's use the substitution method:
Step 1: We have the equation x + y = 8.
Step 2: Solve this equation for one variable in terms of the other. In this case, let's solve for y in terms of x:
y = 8 - x.
Step 3: Substitute y in the second equation with the value found in step 2. We have:
5x - 4 = 8 - x.
Simplifying, we get:
6x = 12.
Step 4: Solve for x:
Divide both sides by 6:
x = 2.
Step 5: Substitute the value of x back into one of the original equations to solve for y. Let's substitute it into the equation x + y = 8:
2 + y = 8.
Subtract 2 from both sides:
y = 6.
Therefore, the smaller number is 2, and the larger number is 6.