Answer:
The hotel at Qakertown charged $5000 before tax while the hotel at Doleystown charged $5,500 before tax
Step-by-step explanation:
In this question, we have a musical band that visited two different towns which hotel charge different amounts at different tax rate. We are now given the total amount in taxes and now asked to calculate what is charged in each of the towns.
Let’s proceed!
Since we do not know the amount charged in each of the towns, let the amount charged at the hotel at Quakertown be $x and the amount charged at the hotel at Doleytown be $y.
Doley charged $500 more then what is charged at Quaker.
Mathematically;
y = 500 + x •••••••••••••••(I)
Let’s now work with the taxes;
Tax rate at Doley is 6% or say 0.06; the amount of tax paid at Doley is thus 0.06y
Tax rate at Quaker is 3% or say 0.03; the amount of tax paid at Quaker is thus 0.03x
Mathematically;
0.06y + 0.03x= 480 •••••••••(ii)
We can substitute i into ii
0.06(500 + x ) + 0.03x = 480
30+ 0.06x + 0.03x = 480
30 + 0.09x = 480
0.09x = 480 - 30
0.09x = 450
x = 450/0.09
x = $5,000
y = 500 + x
y = 500 + $5000 = $5,500
That would be (20+30+56)/200 = 106/200 = 53/100 Answer
Answer:
there are 425 numbers of three digits whose the sum of the digits is even.
Step-by-step explanation:
Option 1:
It is necessary to accomplish one of the next conditions:
(1) all of the digits are even.
(2) exactly 2 of the digits are odd
Then, for the first condition:
4x5x5 = 100 -> this is because the first digit can not be 0.
for the second condition:
(3C1)*5*5*5-1*5*5 =3*125-25=350
where 3C1 is a combination. The 3C1 determines which of the three digits is even, and it is necessary to subtract the numbers under 100 with the other 2 digits odd.
So, there are 450 numbers of three digits whose the sum of the digits is even.
Option 2:
there are 900 three digit number and 5*5*5 =125 has 3 odd numbers and 5*5*5+4*5*5+4*5*5=325 has 1 odd number, so there are 450 numbers of three digits whose the sum of the digitis is odd, so 900-450 whose the sum of the digits is even.
Answer:
If the car is 16 feet long and the model is 1/7 the size of Paul's car, then the model is 27.4 in.
<u>27.4 in.</u>
Step-by-step explanation:
16ft x 12 = 192 inches.
192 / 7 = 27.4 inches.
