Answer:
Let's say we have an expression x * y + z * w, where x, y, z and w are numbers.
We can use the commutative property to change the order of the summands:
x * y + z * w = y * x + w * z = (y + z) * x + w
Since we have a sum of two products, we can use the associative property to combine them:
(y + w) * (x + 15) = 160
By dividing both sides of the equation by 2, we get:
(y + w) / 2 * (x + 15) / 2 = 80
We can then simplify this expression using the distributive property:
(y / 2) + (w / 2) * (x / 2) + (15 / 2)
Since the numbers are all positive, we can cancel out the halves on the left, and combine the remaining terms:
y / 2 + (w / 2) * x + 15 / 2 = 80
Finally, we can simplify this expression by dividing both sides of the equation by the constant fraction:
y / 2 + (w / 2) * x + 15 / 2 = 80
(y / 2) + (w / 2) * (x / 2) + (15 / 2) = 80
Simplifying this expression, we get y / 2 + (w / 2) * x / 2 + 15 / 2 = 40.
By simplifying the last term further, we get:
y / 2 + (w / 2) * x / 2 + 7.5 = 40
Therefore, the equation that simplifies to 160 is this one:
y / 2 + (w / 2) * x / 2 + 7.5
I hope this helps!