Question

A can contains four types of nuts.

• There are 14 more cashews than almonds.
• There are 18 fewer pecans than cashews.
• There are twice as many peanuts as pecans.
There are 38 pecans.
What is the total number of nuts in this can?

Answer 1

To find the total number of nuts in the can, we can solve for the number of almonds using the given information and then calculate the quantities of the other types of nuts. Substituting the value for pecans, we find that there are 208 nuts in total.

Step-by-step explanation:

To find the total number of nuts in the can, we need to determine the quantities of cashews, almonds, pecans, and peanuts. Let's represent the number of almonds as x.

1. Cashews: x + 14
2. Pecans: (x + 14) - 18 = x - 4
3. Peanuts: 2 * (x - 4) = 2x - 8
4. Pecans: 38

From the information given, we know that there are 38 pecans. Substituting this value into the equation for pecans, we get x - 4 = 38, which means x = 42. Therefore, there are 42 almonds, 56 cashews (42 + 14), 34 pecans (42 - 4), and 76 peanuts (2 * (42 - 4)).

To find the total number of nuts in the can, we sum up the quantities of each type of nut: 42 + 56 + 34 + 76 = 208 nuts in total.

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