This last chapter was a very important chapter because it teaches us methods of solving all sorts of real-world problems that involve more than one variable.
Write a wind, water current, or puzzle word problem that you think is challenging. Then solve the problem, providing only the answer in the same post. The most challenging two problems from the class with the correct answers will receive bonus.
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Three digit number is divisible by 10. When the original number is divided by reversed, it is 34. Digits add up to 6. What is the original number.
ReplyDeleteSolution
x + y + z = 6
z = 0
x + y = 6
100x + 10y = 34(10y + x)
100x + 10 y = 340y +34 x
66x -330y = 0
66x + 66 y = 396
-396y = -396
y = 1
x= 5
A: 510
A number between 300 and 400 is forty times the sum of its digits. The tens digit is 6 more than the units digit. Find the number.
ReplyDeleteAnswer: 360
Pg 449 # 31
ReplyDeleteLaura is 3 times as old as Maria was when Laura was as old as Maria is now. In 2 years, Laura will be twice as old as Maria two years ago. Find their present ages.
Answer :
Maria - 12 years old
Laura - 18 years old
David had a few quarters and dimes that was a total of $3.70. David gave Edward as many dimes as he had quarters and as many quarters as he had dimes. When Edward added his coins the total was $2.95. how many quarters and dimes did David have?
ReplyDelete12 quarters
7 dimes
My question is:
ReplyDeleteYour wallet is full of money. You sort them out by value. 100 won coins, 500 won coins, and 1000 won bills are packed up in the wallet. The number of 100 won coins is "a". The number of 500 won coins is "b". The number of 1000 won bills is "c". If "c" is bigger in value than "a" and "b", it works perfectly in the equation : a= b+c+3. In addition, when he arrived at Mr. Jobe's Hotdog Maniac Store, you pay half of your money with 1000 won in change. The hotdog is 9000 won. Find the value of a, b, and c.
(a,b,c are all non-zero positive integers).
Answer: a= 5, b= 1, c= 1
Mimi is 4 years older than Ronald. 5 years ago she was twice as old as he was. Find their ages now.
ReplyDeleteAnswer: Mim is 13 years old
and Ronald is 9 years old
The numerator of a fraction is 3 less than the denominator. If the numerator and denominator are each increased by 1, the value of the resulting fraction is 3/4. Find the original fraction.
ReplyDeleteStep 1 The problem asks for the original fraction.
Step 2 Let n = the numerator of the original fraction and d = the denominator of the original fraction. Then n/d = the original fraction.2
Step 3 Use the facts of the problem to write two equations.
n = d - 3
n + 1/d + 1 = 3/4,or 4(n+1) = 3(d + 1)
Step 4 Simplify the equations and solve.
n = d - 3 - n - d = -3 - 4n - 4d = -12
4(n+1) = 3(d + 1) - 4n - 3d = -1 - 4n - 3d = -1
- d = -11
d = 11
n = d - 3
n = 11 - 3
n = 8
Step 5 The check is left to you.
The original fraction is 8/11.
There are three people, Luke, Lucy, and Mark. Luke's current age equals to the difference of Lucy and Mark's current age. Two years ago, Lucy was 8 times older than Luke. 1 year after, Mark would be 2 times older than Luke. Find Luke's current age.
ReplyDeleteLets say........
Luke = L, Lucy = U, and Mark = M
The first equation would be L = U-M
Two years before, 8(L-2) = U-2
8L-16 = U-2
U = 8L-14
One year after(In the future), 2(L+1) = M+1
2L+2 = M+1
M = 2L+1
To solve this equation, the"substitution method" would be the easiest method to use.
In the equation L = U-M from above, replace U and M.
Replace U with 8L-14
Replace M with 2L+1
So... it would be L = (8L-14) - (2L+1)
L = 8L-14-2L-1
L = 6L-15
5L = 15
L = 3
.........So............ Luke's current age would be three years old.
A boy's age is 3 times less than his mom. His mom is 2 years younger than her husband. The boy is 4 times less than his dad. How old is the boy?
ReplyDelete3b=m
m=d-2
d=4b
3b=d-2
3b=4b-2
b=2
The boy is 2yrs old
Jack is 10 years younger than his teacher, but his teacher's mother is 30 years older than her. Two years ago, teacher's mother's age was twice as much as the teacher. Find the ages of Jack
ReplyDeletej= t-10
m= t+30
m-2= (t-2)2
t+28= 2t-4
24=t
j= 24-10
j- 14
Jack is 14 years old
Oh no wait, that was wrong, sorry.
ReplyDeletem-2= (t-2)2
t+28= 2t-4
t=32
j= 32-10
Jack is 22 years old
A dog is 4times less than a cat. A cat is 4years younger than a monster. The dog is 8times more than monster. How old is dog.
ReplyDeleteC= 4d
C= m-4
M= 8d
4d= 8d-4
d= 2d-1
-d = -1
dog is 1years old
Sophia Yu
ReplyDeleteNext year, Ann will be twice as old as Sean will be. Four years ago, she was three times as old as Sean. How old is Ann?
a+1=2(s+1)
a-4=3(s-4)
a+1=2s+2
a-4=3s-12
a=3s-8
3s-8+1=2s+2
s=9
a=19