Given that a:b = 8:5 and b:c= 3:4
find the ratio a:b:c
Give your answer in its simplest form.
Show all working out.
My work:
1) 5 and 3 both equal to b.
2) 8+5=13/2= 11.5
3)3+4=7/2=3.5
4)11.5+3.5= 15
All my working shown I dont understand this question please help!
Sorry, I don't understand what your "working" is trying to do, but in any case,
8+5≠13/2≠11.5
and so on, so some corrections on your part need to be done.
Given that a:b = 8:5 and b:c= 3:4
What we need to do is to multiply each ratio appropriately so that the "b" match, and is the LCM of the original "b" values.
a:b=8:5=3(8:5)=24:15
b:c=3:4=5(3:4)=15:20
Since "b" in both ratios are 15 (LCM of 5 and 3), we can conclude that
a:b:c=24:15:20
listen to hikari are and watch haikyuu
Well, it seems like you're on the right track, but let me help you understand it better.
First, let's simplify the ratios we have:
a:b = 8:5
b:c = 3:4
To find the ratio a:b:c, we need to find a common value between these two ratios. Since b appears in both ratios, let's make it the same value in both ratios. We can do this by multiplying the first ratio by a factor of 4 and the second ratio by a factor of 5:
(4/5) * (a:b) = 4/5 * 8:4/5 * 5
which simplifies to:
(a:b) = 32:25
(5/3) * (b:c) = 5/3 * 3:5/3 * 4
which simplifies to:
(b:c) = 5:4
Now we have a:b = 32:25 and b:c = 5:4.
To find a:b:c, we need to combine these two ratios. Since b appears in both ratios, we can eliminate it and only focus on a and c. To do this, we can multiply the two ratios together:
(a:b) * (b:c) = 32:25 * 5:4
which simplifies to:
(a:b:c) = 160:100:100
Finally, we can simplify this ratio further by dividing each number by their common factor of 20:
(a:b:c) = 8:5:5
So, the simplest form of the ratio a:b:c is 8:5:5.
To find the ratio a:b:c, we must first find the values of a, b, and c.
Given that a:b = 8:5, we can express this as "a is a multiple of 8, and b is a multiple of 5". Let's assign a value to b for simplicity. In this case, let's assume that b = 5.
Using the ratio a:b = 8:5, we can cross multiply:
8 * 5 = 5 * a
40 = 5a
a = 40/5
a = 8
So, we have found a = 8 when b = 5.
Next, we are given that b:c = 3:4. Based on the previous assumption that b = 5, we can substitute this value into the ratio:
5:c = 3:4
Now we cross multiply again:
3 * c = 4 * 5
3c = 20
c = 20/3
Thus, we have found c = 20/3 when b = 5.
Now we have the values of a, b, and c: a = 8, b = 5, and c = 20/3.
To find the ratio a:b:c, we simply write these values in the order of a, b, and c:
a:b:c = 8:5:20/3
To express the ratio in its simplest form, we need to ensure that the denominator is a whole number. To do this, we can multiply the numerator and denominator of the fraction by 3:
a:b:c = 8:5:20/3 * 3/3
= 8:5:60/9
Now, we can simplify the fraction 60/9 by dividing both the numerator and the denominator by their greatest common divisor, which is 3:
60 ÷ 3 = 20
9 ÷ 3 = 3
Therefore, the simplified ratio is:
a:b:c = 8:5:20/3 = 8:5:20/3 = 8:5:6/1
The final simplified ratio is a:b:c = 8:5:6.
i doent no barbra
wots 1 + 1??????
thx for da help gs