Question

William bought some cashews and walnuts. Spending the same amount of money as William, his twin Jillian bought twice as many cashews and 10 less walnuts. If the cost of one walnut is 2 more than the cost of cashew, then what is the minimum possible number of cashews bought by the twins together?

Answer 1

Answer: 33

Explanation:

Given

The cost of one walnut is 2 more than the cost of a cashew

Jillian bought twice the amount of cashew as William and 10 fewer walnuts

Suppose the price of cashew and walnuts be x and x+2

Assume William bought a cashew and b walnuts

Money spent by Willian

`\Rightarrow W=a(x)+b(x+2)`

Money spent by Jillian

`\Rightarrow J=2a(x)+(b-10)(x+2)`

They spent equal money i.e.

`\Rightarrow ax+bx+2b=2ax+bx+2b-10x-20\\\Rightarrow ax-10x-20=0\\\Rightarrow (a-10)x=20\\\text{Here product of two number is 20 , so both must be greater than 0}\\\therefore a-10>0\\\Rightarrow a>10\\\text{i.e. minimum value of a is 11}`

The amount of cashew both twins bought is a+2a=3a

`\Rightarrow 3a=3* 11=33`