Mike took clothes to the cleaners three times last month. First, he brought 4 shirts and 1 pair of slacks and paid $15.95. Then he brought 7 shirts, 4 pairs of slacks, and 1 sports coat and paid $49.38. Finally, he brought 3 shirts and 1 sports coat and paid $15.46. How much was he charged for each shirt, each pair of slacks, and each sports coat? Mike was charged $ nothing for each shirt, $ nothing for each pair of slacks, and $ nothing for each sports coat.

Each Shirt ≈ $2.49

Each Pair of Slacks ≈ $5.99

Each Sports Coat ≈ $7.99

Step-by-step explanation:

Mike took clothes to the cleaners three times last month.

Let S denotes shirts, P denotes pair of slacks and C denotes sports coat.

First, he brought 4 shirts and 1 pair of slacks and paid $15.95.

Mathematically,

4S + P = 15.95      eq. 1

Then he brought 7 shirts, 4 pairs of slacks, and 1 sports coat and paid $49.38.

Mathematically,

7S + 4P + C = 49.38      eq. 2

Finally, he brought 3 shirts and 1 sports coat and paid $15.46.

Mathematically,

3S + C = 15.46      eq. 3

We are asked to find how much was he was charged for each shirt, each pair of slacks, and each sports coat.

4S + P + 0C = 15.95               eq. 1

7S + 4P + C = 49.38              eq. 2

3S + 0P + C = 15.46               eq. 3

We have 3 equations and 3 unknowns, they can be solved simultaneously using calculator or using online system of equations solver.

Using online system of equations solver yields,

S ≈ $2.49

P ≈ $5.99

C ≈ $7.99

So that means Mike was charge $2.49 for each shirt, $5.99 for each pair of slacks and $7.99 for each sports coat.

false

step-by-step explanation:

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560