Bill buys x items at $3 each, y items at $5 each, and z items at 6 each. If x,y,and z are each multiple of 5 and the total price of the items costing $3 and $5 is 55, which of the following could be the total price of all x +y+z items?

a. 66 b. 80 c. 95 d. 145 d. 150

i got it, thank you for giving the hint. It is d, since after subtracting 55, the only divisible by 6 that has a multiple of 5 is d.

There must be 10 costing $3 and 5 costing $5. That adds up to $55. The number of z's sold must be a multiple of 5 and the amount spent on z's must be a multiple of 6 x 5 = 30.

$145 (d) is a possibility if 15 z's are sold.

To find the total price of all x + y + z items, we need to determine the value of x, y, and z based on the given constraints.

We are told that x, y, and z are each a multiple of 5. Let's assume the values of x, y, and z are denoted as 5a, 5b, and 5c, respectively, where a, b, and c are integers.

Next, we know that x items are bought at $3 each and y items at $5 each, with a total cost of $55. So we can set up the equation:

3(5a) + 5(5b) = 55

Simplifying this equation, we get:

15a + 25b = 55

Dividing both sides by 5, we get:

3a + 5b = 11

Now, we can try plugging in values for a and b to see which option satisfies the equation.

a = 1, b = 2:
3(1) + 5(2) = 3 + 10 = 13 (not equal to 11)

a = 2, b = 1:
3(2) + 5(1) = 6 + 5 = 11 (equal to 11)

Therefore, with a = 2 and b = 1, the equation is satisfied. This means that the value of x + y + z is equal to (5a + 5b + 5c), which is (5(2) + 5(1) + 5(0)) = 10 + 5 + 0 = 15.

Checking the given options, only option (d) 150 is equal to 15. Therefore, (d) 150 could be the total price of all x + y + z items.