There are some peanuts and almonds in a packet. The proportion of peanuts is 2/3 of the total number of nuts in he packet.
(a) What proportion of nuts in the packet are almonds?
(b) What is the ratio of the number of almonds in the packet to the total number of nuts in the packet?
(c) What is the ratio of the number of peanuts to the number of almonds in the packets?
Answer must be three because ratio of almonds is only 3 so mayn't it be
To answer these questions, we need to understand the given information and use some basic math concepts.
Let's assume the total number of nuts in the packet is represented by the variable 'x'.
(a) The proportion of peanuts in the packet is given as 2/3. This means that out of the total 'x' nuts, 2/3 of them are peanuts. To find the proportion of almonds in the packet, we can subtract the proportion of peanuts from 1 (since the total proportion should add up to 1):
Proportion of almonds = 1 - Proportion of peanuts
= 1 - 2/3
= 3/3 - 2/3
= 1/3
Therefore, the proportion of nuts in the packet that are almonds is 1/3.
(b) The ratio compares two quantities. To find the ratio of the number of almonds in the packet to the total number of nuts in the packet, we need to determine the actual number of almonds and the total number of nuts.
Number of almonds = Proportion of almonds * Total number of nuts
= (1/3) * x
= x/3
So, the number of almonds in the packet is x/3.
The ratio of the number of almonds to the total number of nuts is given by:
Ratio = Number of almonds : Total number of nuts
= x/3 : x
= 1/3 : 1
= 1 : 3
Therefore, the ratio of the number of almonds in the packet to the total number of nuts in the packet is 1:3.
(c) The ratio of the number of peanuts to the number of almonds can be found by dividing the number of peanuts by the number of almonds.
Ratio = Number of peanuts : Number of almonds
= (Proportion of peanuts * Total number of nuts) : Number of almonds
= (2/3 * x) : (x/3) (substituting the values from parts (a) and (b))
= (2x/3) : (x/3)
= 2 : 1
Therefore, the ratio of the number of peanuts to the number of almonds in the packet is 2:1.