Every black bicycle in the school yard has a bike bell. Half of all the red bikes have bells. Half of all the bikes with bells are black. There are 40 red bikes and 30 black bikes.
1. If there are 30 black bikes and half of all the bikes with bells are black, how many bikes have bells?
2. How many bikes with bells are either black or red?
3. How many bikes with bells are neither black nor red?
please show me the answer and how you did it thank you! ^^
Answers:
1) 30 = 1/2 b
where b is the number of bikes with bells.
Therefore, b = 60
2) Obviously, there are 30 black bikes with bells. In addition, half of all the red bikes have bells, and there are 40 red bikes.
Therefore,
r = 40/2 = 20
So, add the number of red and black bikes
20 + 30 = 50 bikes with bells
3) If there are 30 black bikes, they all have bells, and half of all the bikes with bells are black, then:
30 = t/2
t = 60 (bikes with bells)
IF there are 50 bikes with bells that are either red or black, then
60-50 = 10 bikes of other colors with bells.
Woah.
1. If there are 30 black bikes (each with a bell), that make up half of the total bikes with bells, there are 60 bikes with bells.
2. If there are 40 red bikes (half of them have a bell: 20) and 30 black bikes (all have a bell: 30) then 50 bikes have bells.
3. If there are 40 red bikes (half of them have a bell: 20) and 30 black bikes (all have a bell: 30) then 50 red and black bikes have bells. Now, in the beginning it said Half of all bikes with bells are black, so 30•2 = 60. So there are 60 bikes with bells total. So: 60-50 = 10 bikes with bells that are neither black nor red.
Let's take a look at each statement, and figure out what we know. Take the last statement first, because it gives us concrete numbers. We'll designate the Color by a capital letter (Black, Red, or X - unknown), and the presence of a bell by a small letter (With, withOut, and Total). We know that the Total will be the number with plus the number without.
40 Red and 30 Black bikes, and some quantity of total bikes.
{Bt} = 30
{Rt} = 40
Every black bike has a bell.
{Bw} = 30
{Bo} = 0
Half of the red bikes have bells
{Rw} = 1/2 {Rt} = 20
Half of all bikes with bells are black.
{Bw} = 1/2 {Xw}
1/2 {Xw} = 30
{Xw} = 60
1) If there are 30 black bikes [Bw=30] and half of all the bikes with bells are black [(1/2)*Xw = Bw] how many bikes have bells?
--Since half of all belled bikes are black, and there are 30 black bikes with bells, doubling the number of black bikes with bells gives us 60 bells.
2) How many bikes with bells are either black [Bw] or red [Rw]?
--There are 30 black bikes with bells. Half of the 40 (meaning 20) red bikes have bells. 30+20= 50 bikes with bells are either red or black.
3) How many bikes with bells [Xw] are neither black [-Bw] or red [-Rw]?
--Since question 1 told us that Xw is 60 and the ones that are black or red are 50; then 60-50=10 bikes with bells are NOT black or red.
Every Black has bell so Bb = 30
Half Red have bell so Rb = 20
Half Red have no bell so R = 20
Half of Total have bell so Tb = T
Now Q1. Bb = 30, and Tb/2 = Bb = 30
=> Tb = 2x30 = 60 Answer.
Q2. Bikes with bell which are either black or red = Bb + Rb = 30 + 20 = 50 Answer.
Q3. Bikes with bell which are neither Black nor are Red = Tb -- (Bb + Rb)
= 60 -- (30 + 20)
= 10 Answer.
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