Final answer:
Nick charges $20 as a flat rate and $6 per lunch in a linear equation y = 20 + 6x. Kayne spends $50 for 5 lunches. If the flat rate is increased to $32, he will need $62 for the same number of lunches.
Step-by-step explanation:
Nick, a personal chef, charges a flat rate of $20 and $6 for each lunch he prepares. To represent the total charge, we can use the equation y = 20 + 6x, where 'y' is the total charge and 'x' is the number of lunches made. The flat rate in this equation, which is $20, represents the initial charge regardless of the number of lunches. It's the amount Nick charges for his availability and basic services before any specific lunch-making begins.
If Kayne buys lunch for himself and four friends, he is buying 5 lunches in total. So, he will spend y = 20 + 6(5) = 20 + 30 = $50 in total. Now, if Nick increases his flat rate by $12, the new flat rate will be $32. The new cost for 5 lunches would be y = 32 + 6(5) = 32 + 30 = $62. Without knowing Kayne's original budget, we cannot determine if he will still be able to afford the lunches for his friends.