Answer: $27.00.
Step-by-step explanation: Usually asking yourself “what quantity or quantities are we trying to find” gives you a good guide as to what quantities to use as the variables. In this case, however, we’re dealing with what is inherently a two-stage problem. If we only knew how much rice costs per lb and how much potatoes cost per lb, then we could easily figure out the desired cost figure. Moreover, the information that we are given seems to be the sort of information that would enable us to figure out cost of rice per lb and cost of potatoes per lb. So here’s the plan:
Stage 1. Figure out (using an appropriate system of equations) the per lb prices for rice and potatoes, respectively.
Stage 2. Use the results from Stage 1 to figure our how much 10 lb of rice and 50 lb of potatoes cost.
Carrying out the plan. You can use either prices in cents or prices in dollars. It doesn’t matter which, but you need to set up your equations consistently. I’m guessing you probably used cost in dollars, so I’ll do that as well.
Stage 1 Solution. Let x = the per-lb cost in dollars for rice. Let y = the per-lb cost in dollars for potatoes. We know that 20 lb of rice and 10 lb of potatoes cost $16.20, so we must have
20x + 10y = 16.20
Similarly, from the given information that 30 lb of rice and 12 lb of potatoes cost $23.04, we find the equation
30x+12y = 23.04.
If you solve this system, you should get x = .60 and y = .42. In other words, rice costs 60 cents per lb and potatoes cost 42 cents per pound.
Stage 2 Solution. The total cost, in dollars, for 10 lb of rice and 50 lb of potatoes will be 10(.60) + 50(.42)
