the sum of two numbers is 42 their prodcut is 185 what are the two numbers. Need to know how to get the answers for a 5th grader
first, find the factors of 185: 5,37
since these are the only two factors, and they add to 42, we're done.
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To solve this problem, you can use algebraic equations. Let's say the first number is "x" and the second number is "y".
According to the problem, we know two pieces of information:
1. The sum of the two numbers is 42:
x + y = 42
2. The product of the two numbers is 185:
x * y = 185
To solve the system of equations, we can use substitution or elimination method. Let's use the substitution method.
Solve equation 1 for x:
x = 42 - y
Substitute this value of x into equation 2:
(42 - y) * y = 185
Simplify equation 2:
42y - y^2 = 185
Rearrange the equation to form a quadratic equation:
y^2 - 42y + 185 = 0
Now, we need to find the values of y that satisfy this quadratic equation. Since the question asks for two numbers, there will be two solutions.
You can either solve this quadratic equation by factoring, completing the square, or using the quadratic formula. For a 5th grader, factoring might be the easiest method.
So, let's factor the quadratic equation:
(y - 5)(y - 37) = 0
Setting each factor to zero to find the solutions:
y - 5 = 0 or y - 37 = 0
Solving each equation:
y = 5 or y = 37
Now that we have found two possible values for y, we can substitute them back into equation 1 to find the corresponding values of x.
For y = 5:
x = 42 - y
x = 42 - 5
x = 37
For y = 37:
x = 42 - y
x = 42 - 37
x = 5
Therefore, the two numbers that satisfy the given conditions are x = 37 and y = 5, or x = 5 and y = 37.