Challenging equations questions (I need working out please) (1 Viewer)

[smithjohn]

a) Steve has a broken calculator. When just turned on, it displays 0. If the + key is pressed it adds 51. If the – key is pressed it subtracts 51. If the × key is pressed it adds 85 and if the ÷ key is pressed it subtracts 85. The other keys do not function. Steve turns the calculator on. What is the number closest to 2003 that he can get using this calculator?

b) A rectangular garden pond has a length 60 cm more than its width. The pond has a 50 cm wide path around its perimeter. If the area of the path is 5.6 m2 , find the width of the pond.

c) A father is concerned about his son’s progress in Mathematics. In order to encourage him, he agrees to give him 10 cents for every problem he solves correctly and to penalise him 15 cents for every problem he gets wrong. The boy completed 22 problems for homework. How many problems did the girl get correct?

d) When a mathematics teacher was asked her age she replied, “One-fifth of my age three years ago when added to half my age last year gives my age eleven years ago.” How old is she?

 

[Eagle Mum]

a) The highest common factor of 85 and 51 is 17. Steve can produce any multiple of 17 by repeatedly pressing +, +, ÷ (+51+51-85 = +17). Since he can only ever add or subtract a multiple of 17, all of the numbers he is able to produce are multiples of 17. When 2003 is divided by 17, the quotient and remainder are 117 r 14. Since 14 is closer to 17 than to zero, the multiple of 17 closest to 2003 is 118 x 17 = 2006.


b) #1. Let w be the width of the pond.
#2. Then, the length of the pond is w + 0.6
#3. Given that the path is 0.5m wide, the length of the path along the long axis is w + 0.6 + 0.5 + 0.5 = w + 1.6
#4. The total area of EACH of these sections of the path is 0.5 ( w + 1.6), but since there are two such sections, on either side of the length of the pond, the combined area of these two sections is w + 1.6
#5. The two short sections of the path alongside the width of the pond each have an area of 0.5w and since there are two such sections, on either side of the width of the pond, the combined area of these two sections is 2x 0.5w = w
#6 Adding the two longer sections & two shorter sections (#4 & #5), the total area of the path is w + 1.6 + w = 2w + 1.6
#7 Since the area of the path is given to be 5.6: 2w + 1.6 = 5.6
Solving equation #7: w = 2.0 The width of the pond is 2.0 metres

c) There isn’t enough information to solve this question. We need to know the final sum of money the son gained from this arrangement. If we had this piece of information, we can then construct simultaneous equations to solve for the number of correct answers.

d) Let x be the teacher’s current age.
Then the word statement can be expressed as the following equation: (x-3)/5 + (x-1)/2 = x-11

Multiplying both sides of the equation by 10 to eliminate fractions:

2(x-3) + 5(x-1) = 10(x-11)
2x -6 + 5x - 5 = 10x - 110
7x - 11 = 10x - 110
99 = 3x
x = 33
The teacher is 33 years old.

 

[Qeru]

a) Steve has a broken calculator. When just turned on, it displays 0. If the + key is pressed it adds 51. If the – key is pressed it subtracts 51. If the × key is pressed it adds 85 and if the ÷ key is pressed it subtracts 85. The other keys do not function. Steve turns the calculator on. What is the number closest to 2003 that he can get using this calculator?

b) A rectangular garden pond has a length 60 cm more than its width. The pond has a 50 cm wide path around its perimeter. If the area of the path is 5.6 m2 , find the width of the pond.

c) A father is concerned about his son’s progress in Mathematics. In order to encourage him, he agrees to give him 10 cents for every problem he solves correctly and to penalise him 15 cents for every problem he gets wrong. The boy completed 22 problems for homework. How many problems did the girl get correct?

d) When a mathematics teacher was asked her age she replied, “One-fifth of my age three years ago when added to half my age last year gives my age eleven years ago.” How old is she?

Who is the girl for c lol