At a bargain store, peyton bought 3 items that each cost the same amount. joe bought 4 items that each cost the same amount, but each was $2.25 less than the items that peyton bought. both peyton and joe paid the same amount of money. what was the individual cost of each person's items? (a) write an equation let x represent the cost of peytons items (b)solve the equation (c)check your solution (d)state the solution in complete sentences

(a) x represents the cost of Peyton's item.

Since, Peyton bought 3 items, total cost paid by Peyton = 3x

It is given that Joe's item is $2.25 less than Peyton's.

Therefore, cost of Joe's item = x - 2.25.

Since, Joe bought 4 items, total cost paid by Joe = 4(x - 2.25).

Since both paid the same amount of money,

3x = 4(x - 2.25)

(b) 3x = 4(x - 2.25)

3x = 4x - 9

3x - 4x = -9

-x = -9

x = 9

(c) Check:

Amount spent by Peyton = 3x = 3(9) = $27.

Amount spent by Joe = 4(x - 2.25) = 4(9 - 2.25) = 4(6.75) = $27.

According to the problem, since both are same, our solution x = 9 is correct.

(d) The solution x = 9 is the cost of each item bought by Peyton and x - 2.25 = 9 - 2.25 = 6.75 is the cost of each item bought by Joe.

1. If it is intersection then it SHOULD be included in both the sets right? Now we know that odd numbers from 1-100 but the second set are multiples of 5 from 50-150! So we mainly need to look for common numbers which are ODD and are a MULTIPLE OF 5 BETWEEN 50 - 100!! So A={51,53,57,59,6199} B={55,60,65,7095} [We stop till 100 because set A has no such element] So what is A ∩ B here? A ∩ B = {All odd numbers and multiples of 5 between 50 - 100}