Tricky math problems? Come have fun!?

Question

1. If 3x +3y + 16 = 40 and x + y = 8
What is x and what is y?

2. The original price of a tomato at local grocery store was decreased by 25%. By what percent must it be increased by to return to its original price?

3. Solve for x in for this equality written in words.
One over one plus (one plus x) over six over eight plus x over ten over eight minus x is equal to the sum of the first fifty integers minus the absolute value of negative six hundred fifty.

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Answer 1

q1
any x and y that add up to 8

q2
3/4*(1+x)=1
x=1/3
=33 1/3%

q3
One over one plus (one plus x) over six over eight plus x over ten over eight minus x is equal to the sum of the first fifty integers minus the absolute value of negative six hundred fifty.

1/1+(1+x)/(6/8+(x/10/8-x))
=(sum of 1st 50 integers)-l-650l

50*51/2-650
=625
=1/1+(1+x)/(6/8+(8x/(10-8x)))
=1/1+(1+x)/(7.5+2x)/(10-8x)
=1/1+(1+x)(10-8x)/(7.5+2x)
=(7.5+2x)/(7.5+2x)+(1+x)(10-8x)
=(7.5+2x)/(7.5+4x-8x^2)
=[15+4x]/[15+8x-16x^2]
=[15+4x]/[5-4x][3+4x]

5^4*[16x^2-8x-15]+4x+15=0

10000x^2-4996x-624*15=0

2500x^2-1249x-2340=0

Answer 2

1. If 3x +3y + 16 = 40 and x + y = 8
What is x and what is y?
There are infinite number of solutions: (x, 8-x) for any x value, since the two equations are the same: y = 8-x.

2. The original price of a tomato at local grocery store was decreased by 25%. By what percent must it be increased by to return to its original price?
.75(1+x) = 1
x = 1/.75 - 1 = 33 1/3%

3. Solve for x in for this equality written in words.
One over one plus (one plus x) over six over eight plus x over ten over eight minus x is equal to the sum of the first fifty integers minus the absolute value of negative six hundred fifty.
1/[1+(1+x)/(8+x)/(10/8) - x] = (1/2)(1+50) - 650

Answer 3

1. x + y = 8

3x +3y + 16 = 40
3 (x+y) = 40 -16
3 (x+y) = 24
3 (x+y) = 3*8

no solution


2. let P = orig price
discounted price decreased by 25%
= 0.75 P

to bring it back to P,
= 0.75 P * (1/0.75)
increase = 1/0.75 = 1.333
or 33.33%


3. One over one plus (one plus x) over six over eight plus x over ten over eight minus x
= 1/1 + (1+x) / 6 / 8 + x / 10 / 8 - x
= 1 + (1+x) / 48 + x / 80 - x
= 1 + 1/48 + x/48 + x/80 - x


is equal to the sum of the first fifty integers minus the absolute value of negative six hundred fifty.
= sum(1st 50 integers) - abs(-650)
= sum(1st 50 integers) - 650

Answer 4

1. If 3x +3y + 16 = 40 and x + y = 8
What is x and what is y?
Analyzing the equations it can be seen that these two equations are parallel. Simplifying 3x+3y+16=40, would give 3x+3y=26 or x+y=26/8. Graphing the two lines, we would see that they don't intersect at a certain point. Thus there is no solution set.ss={ }
2. let x= original price
0.75 x = discounted price
let y= percent increase
(1+y)(0.75x)=x
(1+y)=1/0.75
(1+y)=1.33333
y=0.33333
The price must be increased by 33.33333% to return to its original price.

3.

Answer 5

Since the transform matrix for the two equations isn't invertable, ther is no unique solution.

It must be increased by 33 1/3 %

You really need to find better ways to waste your time.

Doug

Answer 6

1) if first equation is divided by 3
x+y = 16/3 . . . .. equation 1
x+y = 8 . . . . . . . equation 2
there is no solution to this

2) increase it by 25%

3) ?