Could someone help explain a few math problems to me?

Question

I just need someone to explain these three problems to me. I'm really stuck on #3, so be sure to give me a clear explanation on that one.

1. In a certain cereal, the ratio of wheat flakes to raisins to almonds is 14:2:1. If (1/4) cup of cereal contains 5 raisins, how many more wheat flakes than almonds are there in 2 cups of cereal?

2. If 3a=2b and 3b=5c, what is the ratio of a to c?

3. If (ab)/c=7=(rs)/t, r=3a, c=2t, and s=kb, what is k?

Answer 1

1. (1/4) a cup contains 5 raisins, then 2 cups contains 5*8 = 40 raisins. Raisins to almonds is 2:1, so there are 40/2 = 20 almonds. Flakes to raisins is 14:2 or 7:1, so there are 40*7 = 280 wheat flakes. So there are 280 - 20 = 260 more wheat flakes than almonds.

2. If 2b = 5c, b = (5/2)c, Now plug into the first equation
3a = 2(5/2)c, so 3a = 5c, and a/c = 5/3. So the ratio of a to c is 5 to 3.

3. Plug in r = 3a, c = 2t and s = kb into the first two expressions to get:
(ab)/(2t) = 7
(3akb)/t = 7
From the first equation get b=(14t)/a, plug into the second,
(3ak(14t/a))/t = 7
3*14*k = 7
k = 7/42 = 1/6.

Answer 2

Hi,

1. Since the ratio of wheat flakes to raisins is 14:2 and there were 5 raisins in 1/4 cup then there are 7 times as many or 35 wheat flakes in 1/4 of a cup. In 2 cups there would be 8 times as many or 280 wheat flakes. Since the ratio of almonds to raisins is 1:2 and there were 5 raisins in 1/4 cup then there are half as many or 2.5 almonds in 1/4 of a cup. In 2 cups there would be 8 times as many or 20 wheat flakes. The difference between the number of wheat flakes and almonds in 2 cups would be 280 - 20 or 260.

2. Look at the following ratios:

3a = 2b
.........3b = 5c

Multiply the top line by 3 and the bottom line by 2.

9a = 6b
.........6b = 10c

Since the quantity in the middle is the same, it can be dropped out and 9a = 10c. Their ratio is 9:10.

3. If (ab)/c=7=(rs)/t, r=3a, c=2t, and s=kb, then

(ab)/c=7=(rs)/t
(ab)/c=7=(6akb)/c
(ab)/c=7=(6kab)/c
If (ab)/c = 7then (6kab)/c is the same as (6k)ab)/c = (6k)7 or

7 = 42k
k = 1/6


I hope that helps!! :-)

Answer 3

There are twice as many wheatflakes than almonds. if 1/4 cup contains 5 raisins, 1 cup contains 4x5=20 raisins and 2 cups contain 40 raisins and 20 almonds. There are 14 times more wheat flakes than almonds. So, there must be 20x14=280 wheatfalkes in 2 cups. 260 more than raisins.

3. (ab)c=7=rs(t) r=3a c=2t s=kb
(ab)(2t)=7=(3a)(kb)t
2abt=7=3abtk --- (1)
2abt=7
abt=3.5
in (1) 3abtk becomes 3(3.5)k=7
10.5k=7
k=7/10.5

2. 3a=2b -- (1)
3b=5c
b=5c/3
(1) becomes 3a=2(5c/3)
3a=10c/3
9a=10c
9:10

Answer 4

14 wheat flakes for each 2 raisins for each 1 almond.

in 1/4 cup there are 5 raisins

35 wheat flakes for each 5 raisins for each 2.5 almond is in the ratio of 14:2:1. (multiply each number by 2.5)

in 2 cups, there are 8 times as many objects as in 1/4 cup, so multiply each number by 8

280 wheat flakes for each 40 raisins for each 20 almonds

280 wheat flakes and 20 almonds means that there are 240 more wheat flakes than almonds.

Answer 5

1.) 1/4 cup = 35 W +5R +2.5A, so
2cups = 280W +40R +20A. so
There are 280/20 = 14 X as many wheat flakes as Almonds.
There are 260 more wheat flakes than almonds.

2.) 3a= 2b and 3b = 5c
a= 2b/3 and c = 3b/5
So a/c = 2b/3* 5/(3b) = 10/3

3) If (ab)/c=7=(rs)/t, r=3a, c=2t, and s=kb, what is k
s= 7t/r and b= 7c/a
k= s/b = (7t/r)(a/(7c)) = at/rc
k = at/[(3a)(2t)] = 1/6

Answer 6

ab/c = rs/t
therefore
s = abt/cr

using r=3a
s=abt/c3a = bt/3c

using c=2t
s = bt/3(2t) = bt/6 = (t/6)b

using s=kb
s=(t/6)b = kb
therefore k = t/6