# Category: System of linear equations

## Challenging System of Linear Equations problem 1

At Nuts supermarket, a discount is offered on Almonds, Cashew and Walnuts if more than a certain weight of it is bought. On a particular grocery shopping trip, King Kong bought a total of 12 kg of nuts as follows:

Types of Nut | Price per kg ($) | Discount offered |

Almond | 14 | 20% for more than 6 kg bought |

Cashew | 9 | 15% for more than 3 kg bought |

Walnuts | 11 | 10% for more than 2 kg bought |

King Kong bought at least 3.5 kg of each type of nut and spent $124.03 after an overall discount of $10.17. Find the weight of each type of nut King Kong bought from the supermarket.

**Solution**

We know that discount is obtained from the purchase of cashew and walnuts, since the amount bought is at least 3.5 kg of each type. However, we do not know whether any discount is obtained for the purchase of almonds.

Therefore, we make the assumption that the amount of almonds bought is less than or equal to 6kg, and hence no discount. If the solution turns out to be between 3.5 to 6kg inclusive, we accept the solution. Else we reject and change the assumption to almonds bought is greater than 6kg, reformulate and solve the equations again.

Let a, b and c be the number of kg of almonds, cashew and walnuts bought respectively.

Therefore a+b+c= 12 (Eqn 1)

14a+b(0.85×9)+c(0.9×11)=124.03

14a+7.65b+9.9c=124.03 (Eqn 2)

0.15x9b+0.1x11c=10.17

1.35b+1.1c= 10.17 (Eqn 3)

Solving the 3 equations with GC,

a= 3.8 , b=4.6, c=3.6

Since a is between 3.5 to 6, our assumption and hence solution is valid.

King Kong bought 3.8 kg of almonds, 4.6 kg of cashew and 3.6 kg of walnuts.