The larger of two positive integers is five more than twice the smaller integer. The product of the integers is 52. Find the integers. Must have an algebraic solution.

In a trapezoid, the smaller base is 3 more than the height, the larger base is 5 less than 3 times the height, and the area of the trapezoid is 45 square centimeters. Use an algebraic solution to find the height, in centimeters, of the trapezoid.

The height of the trapezoid is centimeters.

The sum of two integers is 29. The larger of the two integers is 5 more than 2 times the smaller integer. What are the integers?

To solve this problem algebraically, let's assume that the smaller integer is represented by 'x', and the larger integer is represented by 'y'.

According to the problem, the larger integer is five more than twice the smaller integer. This can be represented as:

y = 2x + 5

The product of the integers is 52. We can express this as:

xy = 52

Now, we have a system of two equations with two variables:

1) y = 2x + 5
2) xy = 52

We can substitute equation 1) into equation 2) to solve for 'x':

x(2x + 5) = 52

Expanding and simplifying:

2x^2 + 5x = 52

Rearranging the equation by subtracting 52 from each side:

2x^2 + 5x - 52 = 0

Now, we can solve this quadratic equation. Factoring or using the quadratic formula are two possible methods.

Factoring, we get:

(2x - 13)(x + 4) = 0

This gives us two possible values for 'x': x = 13/2 or x = -4.

However, since we are looking for positive integers, the value x = 13/2 is not valid. Thus, the only solution is x = -4.

Now, we can substitute this value of 'x' back into equation 1) to find the corresponding value of 'y':

y = 2(-4) + 5
y = -8 + 5
y = -3

Therefore, the two positive integers that satisfy the given conditions are 'x' = 4 and 'y' = 3.

Thus, the solution is x = 4 and y = 3.

?I was wondering if you could tell me

Let x stand for one integer and 2x + 5 stand for the other.

The formula you would work with would be:

x(2x+5) = 52

I hope this helps. Thanks for asking.