can someone please help me with math questions..please..=[please!!?

Question

1.supppose the central perk coffee shop sells a cup of espresso for $2.00 and a cappuccino for $2.50.on friday Destiny sold 30 more cups of cappucino than expresso for a total of$178.50 worth of espresso and cappucino.how many cups of each were sold?

2.Th3 yankee clipper leaves the pier at 9:00 am at 8 knots (nautical miles per hour)a half hour later,the river rover leaves the pier in the same direction traveling at 10 knots.at wat time will the river rover overtake the yankee clipper?

3.if 4/5 of 3/4=2/5 of x/4..find value of x

Answer 1

1. let x=number of espresso sold
let x+30=number of cappucino sold
2x+2.5(x+30)=178.50

2. the clipper can travel 8 nautical miles an hour, so it traveled 4 nautical miles in half an hour. to calculate how long it took the rover to travel 4 nautical miles, divide 4 nautical miles by 10 nautical miles per hour. so 4/10=0.4 hr or 24 min

3. (4/5)(2/5)=(2/5)(x/4)
8/25=(2/5)(x/4)
4=x/4
x=16

Answer 2

1. Let's call the number of cups of espresso E and the number of cups of cappucino C.

So, the total sold is $2.00 * E + $2.50 * C which equals $178.50.
We also know that C = E + 30
So,
2 * E + 2.5 * (E+30) = 178.50
2 * E + 2.5 * E + 75 = 178.50
4.5 * E = 103.50
E = 103.5 / 4.5
E = 23
C = E + 30
C = 23 + 30
C = 53

Therefore, there were 23 cups of espresso and 53 cups of cappucino sold.

2. The rover goes 2 nautical miles per hour faster than the clipper. The clipper has gone 8 nautical miles per hour for half an hour, so it has gone 4 nautical miles. The rover will close that 4 nautical mile gap at a rate of 2 nautical miles per hour, so it will take 2 hours.

3. Remember that "of" generally means "times", so you can translate that sentence to be:

4/5 * 3/4 = 2/5 * x/4

Just multiply numerators and demoninators and you get.

12/20 = 2x/20

Multiply both sides by 20

12 = 2x

Divide by 2

6 = x

Answer 3

1.let x=the number of espressos sold
x*2+(30+x)*2.5=178.50
4.5x+75=178.5
4.5x=103.5
x=23
central perk sold 23 cups of espresso and 53 cups of cappucino.

2.let x=the amount of time in hours the river rover needs to catch the yankee clipper (not including the half hour head start)
.5*8+8x=10x
4+8x=10x
2x=4
x=2
the rover will overtake the clipper in 2 hours

3.
4/5 * 3/4=2/5 * x/4
3/5=x/10
x=6

Answer 4

Just transform in equations :
1) x number of expresso :
2 x+ 2.5 (x+30) = 178.5
4.5 x = 103.5
x = 23
23 expressos
53 capu
2) let be t the time after 9 am in hour
8 t = 10 (t-0.5)
5 = 2t
t = 2.5
At 11:30 am
3) 4/5 3/4 = 2/5 x/4
12/20 = 2/5 x/4
12/2 = x
6 = x

Answer 5

tcwps, bad answer on #2: The RELATIVE speed between the 2 ships is only 2 k, so the 4nm must be divided by 2, not 10 giving an answer of 2 hr, not 0.4 hr.

It actually travels 20 nm to overtake the clipper, a distance that takes the clipper 20/8 = 2.5 hr to navigate.