karen decorated her mother's birthday cake. one-third of candles are pink, three-eights are yellow, one-quater are blue and the two remaining candles are white. calculate
(a). the fraction of candles that are white.
(b). the total number of candles on the cake.
Need answer for a and b. PLEASE!!!
total number ---- x
(x/3 + 3x/8 + x/4) + 2 = x
(8x/24 + 9x/24 + 6x/24) + 2 = x
23x/24 + 2 = x
before going further, 1/24 of the candles must be white
and x/24 = 2
x = 48
check:
there were 48 candles,
1/3 pink ---- 16
3/8 yellow --- 18
1/4 blue ----- 12 , total sofar = 46
leaving 2 whites
my answer is correct
Oh, birthdays, the perfect excuse to light a bunch of small, flammable sticks and stick them in a baked good! Now, let's calculate this colorful candle conundrum, shall we?
(a) The fraction of candles that are white:
Let's break this down step by step. We know that one-third of the candles are pink, three-eighths are yellow, and one-quarter are blue. So, if we add those fractions together, we get:
1/3 + 3/8 + 1/4 = (8/24) + (9/24) + (6/24) = 23/24
So, collectively, 23 out of 24 candles are accounted for. The remaining candle or two must be white. Hence, the fraction of candles that are white is:
1/24 or simply 1 out of 24.
(b) The total number of candles on the cake:
Now that we know the fraction of white candles, we can determine the total number of candles on the cake. Given that there are 24 equal parts for the candles in total, and we know that two parts are white, we can set up the equation:
2 parts = 24 candles
Simplifying it, we find:
1 part = 12 candles
Therefore, the total number of candles on the cake would be the sum of all the parts:
24 parts = 24 x 12 candles = 288 candles!
So, Karen went all out for her mother's birthday with a whopping 288 candles! Keep a fire extinguisher nearby just in case things get too hot to handle.
To calculate the fraction of candles that are white and the total number of candles on the cake, we need to add the fractions of each colored candle together.
First, let's calculate the fraction of candles that are white.
Given:
- One-third of candles are pink,
- Three-eighths are yellow,
- One-quarter are blue, and
- The two remaining candles are white.
To find the fraction of white candles, we need to subtract the sum of fractions of pink, yellow, and blue candles from 1 (since the remaining candles are white).
Fraction of pink candles = 1/3
Fraction of yellow candles = 3/8
Fraction of blue candles = 1/4
Sum of fractions (pink + yellow + blue) = 1/3 + 3/8 + 1/4
To add these fractions, we need a common denominator, which in this case is 24. Converting the fractions to have this common denominator, we have:
Sum of fractions = (8/24) + (9/24) + (6/24) = 23/24
Since the remaining candles are white, we can subtract this sum from 1:
Fraction of white candles = 1 - 23/24 = 1/24
Therefore, the fraction of candles that are white is 1/24.
Now let's calculate the total number of candles on the cake. We need to know the specific quantity. Could you provide the quantity of candles?
To solve this problem, we need to find the fraction of candles that are white and the total number of candles on the cake.
(a) To find the fraction of candles that are white, we need to subtract the fractions of candles that are pink, yellow, and blue from 1, because the sum of all fractions should equal 1.
The fraction of candles that are pink is one-third, which can also be written as 1/3.
The fraction of candles that are yellow is three-eighths, which can also be written as 3/8.
The fraction of candles that are blue is one-quarter, which can also be written as 1/4.
To find the fraction of candles that are white, we subtract the sum of the fractions of pink, yellow, and blue candles from 1:
1 - (1/3 + 3/8 + 1/4)
To calculate this expression, we need to find the least common multiple (LCM) of the denominators 3, 8, and 4, which is 24.
First, we convert each fraction to have a common denominator of 24:
(8/8)(1/3) + (3/3)(3/8) + (6/6)(1/4)
8/24 + 9/24 + 6/24
Now, we can add the fractions together:
(8 + 9 + 6)/24
23/24
Therefore, the fraction of candles that are white is 23/24.
(b) To find the total number of candles on the cake, we need to add up the fractions of pink, yellow, blue, and white candles.
The total fraction of candles (including white) is 1, so:
1 = 1/3 + 3/8 + 1/4 + white fraction
Substituting the value obtained for the white fraction in part (a), we get:
1 = 1/3 + 3/8 + 1/4 + 23/24
To calculate this expression, again we need to find the LCM of the denominators 3, 8, 4, and 24, which is 24.
Converting each fraction:
(8/8)(1/3) + (3/3)(3/8) + (6/6)(1/4) + (1/24)(23/24)
8/24 + 9/24 + 6/24 + 23/576
Now, we can add the fractions together:
(8 + 9 + 6 + 23)/24
46/24
Simplifying the fraction, we get:
23/12
Therefore, the total number of candles on the cake is 23/12.