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Topic: **What are the problem solving strategies****Question:**
40 people charter a boat at a cost of $15 dollars each.They're told that for every additional person they can get to go, the price of each ticket will be reduced by 25 cents, provided the total doesn't exceed 60. The net income of the boat operator was 6.25...how many ppl took the boat ride?

July 19, 2019 / By Ginger

What I usually do when solving this type of problems is making some examples until I understand what is going on. So let's see what happens with 40, 41, 42, 43, 59, 60, 61 (to see why the boat operator limits the people at 60. #ppl . . . . . .$ ticket . . . . . net income . . . . . .operation 40 . . . . . . . . 15 . . . . . . . . 600 . . . . . . . . . . 40*15 41 . . . . . . . . 15-.25 . . . . . 604.75 . . . . . . . . 41*14.75 42 . . . . . . . . 14.75-.25 . . . 609. . . . . . . . . . . 42*14.50 43 . . . . . . . . 14.50-.25 . . . .612.75 . . . . . . . . 43*14.25 44 can you write row 44? if you see the operation is the number of people in addition to the 40 original guys, multiplied by the price of the ticket that has the .25 discount per person. If you see this, you can build the next (general) row: #ppl . . . . . $ ticket . . . net income . . . . . . operation 40+x . .. . . 15-.25x . . .(40+x)*(15-.25x) . . . (40+x)*(15-.25x) If you wonder why the net income and the operation columns are the same, it is because the question you are asked is about how to get the 625 dollars, and you are asked how (which refers to how many people, min 40 max 60). Try filling the next rows #ppl . . . . . .$ ticket . . . .net income . . . . . . . . operation 59 . . . . . . . . . . . . . . . . 604.75 60 . . . . . . . . . . . . . . . . 600 61 I hope this helped you to set a strategy to solve this kind of problems. Now about the particular solution to the problem try reconstructing these rows: #ppl . . . . . . . $ ticket . .. . . . . net income . . . . . operation 49 50 51

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Did you like the answer? We found more questions related to the topic: **What are the problem solving strategies**

The two equations (assuming you mean to say 1 sandwich and one drink is $7.50): s+d = 7.50 5s + 2d = 18 Pick an equation and solve for a variable, s = 7.50 - d Then plug what you get in the other equation and solve for the variable. 5(7.50 -d) + 2d = 18 37.5 - 5d + 2d = 18 -3d = -19.5 d =6.50 Now plug that answer back into the first equation solved. s = 7.50 - d s = 7.50 - 6.50 s =$1 So each sandwich is one dollar.

Your first sentence doesnt make sense b/c you have "sandwicheS and 1 drink is 7.50"... but i'll just assume you meant one sandwich... You have two unknowns and therefore need two equations: 1. S + D = 7.50 (where S = sandwiches and D = drinks) 2. 5S + 2D = 18 multiply equation 2 by -2 and add the equations: -2S - 2D = -15 5S + 2D = 18 ------------------ 3S = 3 S = $3 Therefore, each sandwhich is $3. For fun: 3 + D = 7.50 D = 4.50

More like xs + 1d =7.50 5s + 2d = 18.00 Is the first sentence of your problem correct? You have 3 unknowns here x,s,d and just two equations. Not solvable.

This problem could be solved only if you assume discount will apply from the 1st person instead of the 41st. C =n.(15-0.25n ) , where c is the cost and n is the number of the people 6.25=15n - 0.25n² n² - 60n + 25 =0 n = 30 ± 29.58 therefore 60 people will ride the boat.

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1. A bedroom set takes up 21 square meters. A living room takes up 42 square meters. The company has 546 square meters of space. Therefore: 21x + 42y ≤ 546 since the company can't display more than they have space for. Answer: 21x + 42y ≤ 546 2. Make some more inequalities to determine your feasible region: x ≥ 6 y ≥ 5 Graph these two equations and the equation from before, and find the value of the corner points. The maximum profit will ALWAYS be found on one of the corner points. CORNER POINTS: (5, 10.5) (5, 5) (16, 5) You can't sell part of a living room set, so that solution is automatically thrown out. Plug the other two into a profit statement: 10000x + 18000y = P Plugging the values in shows that selling 16 bedroon sets and 5 living room sets will maximize the profit. Answer: 16 bedroom sets and 5 living room sets Hope this helps~

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