4 Algebra 1 Word Problems?

Question

I need to know how to solve these problems. Any help is greatly appreciated.

6.) Bob can mow 1/3 of his lawn in one hour. Jack can mow 1/5 of Bob's lawn in two hours. How fast can they mow Bob's lawn if they mow the lawn together?

7.) Carl is the same age as Lenny. Homer is three years older than Carl and Lenny. Moe is seven years older than Homer. Their ages combined is 153. What is everybody's individual age?

10.) A video rental store offers eight dollars a video for non-members and four dollars per video for members. Members however, have to pay a monthly fee of twenty-four dollars. How many videos must a member rent per year to break even without non-members?

11.) The gas station is having a deal, if you buy a $10 car wash, you get $.10 off per gallon of gasoline you buy. If gasoline costs $3.30 per gallon, how many gallons must you buy to justify that getting the carwash is a better deal?

Answer 1

6.) Bob can mow 1/3 of his lawn in one hour. Jack can mow 1/5 of Bob's lawn in two hours. How fast can they mow Bob's lawn if they mow the lawn together?

Bob mows at 1 lawn/3 hours = 1/3 lph
Jack mows at 1lawn / 10hours = 1/10 lph

add their speeds together:
1/3 + 1/10 = 10/30 + 3/30= 13/30 lph (together)

1 lawn / (13/30 lph) = 30/13hours = 2 & 4/13 hr
= 2.3077... hours

7.) Carl is the same age as Lenny. Homer is three years older than Carl and Lenny. Moe is seven years older than Homer. Their ages combined is 153. What is everybody's individual age?


C = L = H-3
M = H+7

C + L + H + M = 153
(H-3) + (H-3) + H + (H + 7) = 153
4H +1 =153
4H = 152
H = 38
C = 35
L = 35
M = 45

35
35
38
45
___
153




11.) The gas station is having a deal, if you buy a $10 car wash, you get $.10 off per gallon of gasoline you buy. If gasoline costs $3.30 per gallon, how many gallons must you buy to justify that getting the carwash is a better deal?

$10 = 100 * .10
meaning 100 gallons bought would "pay for" the carwash

Answer 2

In doing any of these problems you need to know the principle employed in your answer.

6. Output = lawn/hr x time
Bob can do 1/3 lawn per hour
Jack can mow 1/10 lawn per hour.
Let t= time
1 Lawn = 1/3 t + 1/10 t
Solve for t

7. Sum of ages = 153
Let lenny be L
Let carl be L
Let homer be (L+3)
Let moe be (L+3+7)
Now solve.

10. Break point: Cost of fee+rentals for member= cost of rentals for non-members.
Let V be MONTHLY video rentals
Monthly basis :member = 24+4V
non member=8V
Solve for V for month
Mult by 12 for problem answer

11. Pretty much the same deal as above.
Let G be gallons of gas to break even with carwash
Buy gas without carwash= 3.30 G
Buy gas with carwash = 10 + 3.20 G
Solve for G

Answer 3

6. 1/3+1/10= 13/30 gives you how much they mow together in one hour. 30/13~2.31. So Jack and bob mow it together in about 2 hours and 18 minutes.

7. x+x+(x+3)+(x+10)=153
4x+13=153
4x=140
x=35
Carl=35, Lenny=35, Homer= 38, Moe=45

10. I am sorry but the current wording of the question doesn't make sense

11. 3.20x +10=3.30x
10=.10x
x= 100 gallons
At 101 gallons the car wash is a better deal.

Answer 4

7) Carl=x
Lenny=x
Homer=x+3
Moe=x+3+7

x+x+x+3+x+3+7=153
4x+13=153
4x=140
x=35
Carl and Lenny are 35, Homer is 38, Moe is 45.

11) .10x=10.00
x=100
if you buy 100 gallons of gasoline, you would save 10.00 on gas making your car wash "free"

10) x=the number of videos

4x+24=8x
subtract 4x from both sides
24=4x
x=6

If a member and a nonmember rent 6 videos per month they will both be spending $48 per month

To break even for a year it would be 6X12=72 videos per year to break even

6) Bob takes 3 hours to mow his lawn
1/3+1/3+1/3= the whole lawn or 3 hours since it takes him 1 hr. to do 1/3

Jack takes 10 hours to mow Bob's lawm
1/5+1/5+1/5+1/5+1/5=the whole lawn or 10 hours since it takes him 2 hrs. to do 1/5

multiply their times (3X10) and divide by the sum of their time (3+10) to get the answer.

3X10/(3+10)=
30/13=
2.3077 hours to cut the lawn together

Answer 5

R = 2 x S R - 4 = a million + 3 x (S - 4) 2 x S - 4 = a million + 3 x (S - 4) 2 x S - 4 = a million + 3 x S - 3 x 4 upload 11 to both aspects 2 x S + 7 = 3 x S subtract 2 x S from both aspects 7 = S Sarah is 7 Ryan is 14 4 years contained in the previous, Ryan replaced into 10 and Sarah replaced into 3 So, Ryan replaced proper into a million extra helpful than 3 x 3 Rex, in Indiana

Answer 6

7)
Carl = x
Lenny = x
Homer = x + 3
Moe = (x + 3) + 7
C + L + H + M = 153
x + x + (x + 3) + (x + 10) = 153
4x + 13 = 153
4x = 153 - 13
4x = 140
x = 140: 4
x = 35
Answer:
Carl: 35; Lenny: 35; Homer: 38 and Moe: 45.
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