mathhelper
answered
.3x + y = 64
sub in the first:
.3x + 30-x = 64
solve for x, then sub into y = ....
Explain Bot
answered
1. "The sum of two is 30": This means that if you add the two numbers together, the result is 30.
Let's call the two numbers x and y. So, we have the equation: x + y = 30.
2. "3 times the first number added to the second number is 64": This means that if you multiply the first number by 3 and then add the second number, the result is 64.
Mathematically, we can write this as: 3x + y = 64.
Now we have a system of two equations with two unknowns. We can solve this system using the method of substitution or elimination.
Let's solve it using the method of substitution:
Step 1: Solve one equation for one variable in terms of the other variable.
From the first equation, we can isolate one variable, y, in terms of x: y = 30 - x.
Step 2: Substitute the expression for y into the second equation.
In the second equation, replace y with (30 - x): 3x + 30 - x = 64.
Step 3: Simplify and solve for x.
Combine like terms: 2x + 30 = 64.
Subtract 30 from both sides: 2x = 64 - 30 = 34.
Divide both sides by 2: x = 34 / 2 = 17.
Step 4: Solve for y.
Substitute the value of x (which is 17) back into the first equation: 17 + y = 30.
Subtract 17 from both sides: y = 30 - 17 = 13.
Therefore, the two numbers are x = 17 and y = 13.
Step-by-Step Bot
answered
According to the problem statement, the sum of two numbers is 30, so the second number would be 30 - x.
The problem also states that 3 times the first number added to the second number is 64:
3x + (30 - x) = 64
Now, we can solve this equation to find the value of x.
Combining like terms:
3x + 30 - x = 64
Combine x terms:
2x + 30 = 64
Subtract 30 from both sides:
2x = 34
Divide both sides by 2:
x = 17
Therefore, the first number is 17.
