Question 1190592: on monday, revlien paid 66 pesos for 3 doughnuts and 2 cups of coffee. on tuesday, she paid 69 pesos for 2 doughnuts and 3 cups of coffee. how much did he pay for 1 doughnut and 1 cup of coffee on a wednesday?
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52847)   (Show Source):
You can put this solution on YOUR website! .
on monday, revlien paid 66 pesos for 3 doughnuts and 2 cups of coffee.
on tuesday, she paid 69 pesos for 2 doughnuts and 3 cups of coffee.
how much did he pay for 1 doughnut and 1 cup of coffee on a wednesday?
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This problem is intended for mental solution.
Add her purchases on Monday and Tuesday:
she bought 3+2 = 5 doughnuts and 2+3 = 5 cups of coffee, in total,
spending 66 + 69 = 135 pesos.
HENCE, one doughnut and one cup of coffee cost 1/5 of it, i.e. 135/5 = 27 pesos.
ANSWER. On Wednesday, she must pay 27 pesos.
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Solved.
Notice that I did not solve any systems of equations.
I even did not write them.
It is a classic type of problems, that seem to be solved
using equations, but actually MUST be solved mentally.
Solving mentally is a GOOD STYLE solving such problems.
It is what the teachers expect to get from their students,
when they give them such problems.
It is what the interviewers expect to get from the candidates
when they interview them somewhere in Microsoft or Google.
But the final goal of teachers, when they give such problems, is to develop
the student's mind FLEXIBLE and CREATIVE, instead of making it dogmatic.
Answer by math_tutor2020(3817)  (Show Source):
You can put this solution on YOUR website!
d = cost of 1 doughnut
c = cost of 1 coffee
costs are in pesos
Setting up the cost for Monday
3d = cost of 3 doughnuts
2c = cost of 2 coffees
3d+2c = total cost of the 5 items overall
3d+2c = 66 pesos
Let's solve for c
3d+2c = 66
2c = 66-3d
c = (66-3d)/2
c = (66/2)-(3d/2)
c = 33 - 1.5d
I'll use this later on.
Setting up the cost for Tuesday
2d = cost of 2 doughnuts
3c = cost of 3 coffees
2d+3c = total cost of these 5 new items
2d+3c = 69 pesos
Apply substitution
2d+3c = 69
2d+3( c ) = 69
2d+3( 33-1.5d ) = 69 ... c replaced with 33-1.5d
2d+99-4.5d = 69
-2.5d = 69-99
-2.5d = -30
d = -30/(-2.5)
d = 12
It costs 12 pesos for 1 doughnut
c = 33 - 1.5d
c = 33 - 1.5(12)
c = 33 - 18
c = 15
It costs 15 pesos for 1 coffee
Check for Monday:
3d+2c = 66
3*12+2*15 = 66
36+30 = 66
66 = 66 that works out
Check for Tuesday:
2d+3c = 69
2*12+3*15 = 69
24+45 = 69
69 = 69 that works out as well
We've confirmed we have the correct unit prices for each food item.
For Wednesday, she bought 1 doughnut and 1 coffee
So the amount paid is d+c = 12+15 = 27 pesos
This excludes any kind of tax or extra surcharges.
Answer: 27 pesos
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