I need help with these algebra problems?

Question

They are story problems that need to be solved with 2 variables and 2 equations. If you can at least give me them equations, that's good. if you can help with any more. i would appreciate it.

A video disk rental company charges a fixed amount for the first two days of a rental and an additional charge for each day thereafter. juan paid 19.50 for a disk that he kept 6 days. and tom paid 27.00 for a disk that he kept for 9 days. how much would it cost to rent a video disk for ten days from the same company.

Erik has 50 coins, all nickels, dimes, and quarters. they are worth 3.60 all together. there are two more dimes than quarters and four times as many nickels as the combined number of dimes and quarters. how many of each kind of coin does erik have?

The sum of the present ages of pam, sue and jim is 63 years. the age of pam is 3 years ago is the same as jim's age 2 years from now. the sum of pam's present age and the ages of sue and jim three years ago is one more than twice the age that pam will be in two years. how old are pam, sue, and jim now

Answer 1

Fixed charge (y) in terms of daily charges (x)—2 equations:

y + x(6 - 2) = 19.50

y + 4x = 19.50

y = 19.50 - 4x



y + x(9 - 2) = 27

y + 7x = 27

y = 27 - 7x



Charge per day after 2 days:

19.50 - 4x = 27 - 7x

3x = 7.50

x = 2.50



Fixed charge:

= 19.50 - 4(2.50)

= 19.50 - 10.00

= 9.50



Total charge for 10 days:

= 9.50 + 2.50(10 - 2)

= 9.50 + 2.50(8)

= 9.50 + 20.00

= 29.50



Answer: 29.50 is total charge if video disk is kept for 10 days.

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No. of quarters—q:

10(q + 2) + 25q + 5(4[q + q + 2]) = 360

2(q + 2) + 5q + 4(2q + 2) = 72

2q + 4 + 5q + 8q + 8 = 72

15q = 60

q = 4



No. of dimes:

= 4 + 2

= 6



No. of nickels:

= 4(4 + 6)

= 4(10)

= 40



Answer: 4 quarters, 6 dimes & 40 nickels

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1st equation—age of Pam (p) in terms of ages of Sue (s) and Jim (j):

p + s + j = 63

p = 63 - s - j



2nd equation—age of Jim (j) in terms of age of Sue (s), substitute p:

63 - s - j - 3 = j + 2

2j = 58 - s

j = 29 - 0.5s



1st equation—age of Pam (p) in terms of age of Sue (s), substitute j:

p = 63 - s - 29 + 0.5s

p = 34 - 0.5s



3rd equation—age of Sue (s), substitute p and j:

34 - 0.5s + s - 3 + 29 - 0.5s - 3 = 2(34 - 0.5s + 2) + 1

56 = 2(36 - 0.5s)

56 = 72 - s

s = 16



1st equation—age of Pam (p), substitute s:

p = 34 - 0.5(16)

p = 34 - 8

p = 26



2nd equation—age of Jim (j), substitute s:

j = 29 - 0.5(16)

j = 29 - 8

j = 21



Answer: Pam is 26; Sue is 16 & Jim is 21.

Answer 2

1) x = fixed charge, y = additional charge

Juan-

2x + 4y = 19.50

Tom-

2x + 7y = 27.00



Subtract equations from each other



2x-2x+4y-7y = -7.50

-3y = -7.50

y = 2.50 (which is the charge per day past the first 2 days)

Plug y back in each equation:

Juan-

2x + 4*2.50 = 19.50

2x + 10 = 19.50

2x = 9.50

x = 4.75 (which the charge for the first 2 days)

Tom:

2x + 7*2.50 = 27

2x + 17.50 = 27

2x = 9.50

x = 4.75 (so both equations check out)



To rent a video for 10 days

(2*4.75) + (8*2.50) = 9.50 + 20 = 29.50 (cost to rent 10 days)



2) x = quarters , x+2 = dimes, 4(x+x+2) = nickels

Number of coins-

x + x + 2 + 4(x+x+2) = 50

2x+2+4x+4x+8 = 50

10x+10=50

10x=40

x=4

So there are 4 quarters, 6 dimes (2 more dimes than quarters), and 40 nickels (4 times the amount of dimes and quarters)

4 * .25 = 1.00

6 * .10 = .60

40 * .05 = 2.00

adds to 50 coins equaling 3.60



3) So Pam is 5 years older than Jim

x = Jim's age, x + 5 = Pam's age, y = Sue's age

x + x + 5 + y = 63

2x + y = 58



2nd part of problem -



Pam's age + Sue's age three years ago + Jim's age three years ago = 2 * (Pam's age 2 years in future) + 1



x + 5 + y - 3 + x - 3 = 2(x+5+2) + 1

2x + y - 1 = 2x + 10 +4 + 1 (add all together)

y = 16 (Sue's age)



Plug back into equation

2x + 16 = 58

2x = 42

x = 21 (Jim's age)

x + 5 = 26 (Sue's age)



21+26+16= 63



My answers have been copied BTW by some of the earlier ones lol.

Answer 3

(1) Lets say rent is X for first two days and Y for everyday after that...



Juan X + 4y = 19.50

Tom X + 7y = 27



Now solve the equations and find X & Y and put it in the equation below.



10 days rent = X + 8Y====>





(2) X Nickles, Y Dimes and Z Quarters



5X + 10y + 25z = 360 (Cents) ---------(1)

y-2 = z ----------(2)

x = 4(y+z) ----------(3)



Solve the equation above and you should have the answers....







(3) Pam (x) + Sue (y) + Jim (Z) = 63



x-3 = z+2 == x = z+5 ---------(1)

x+(y-3)+(z-3) = 1+2(x+2) ---------(2)

x + y + z = 63 ------------------------(3)



Solve the three equations above and you should have the answer.

Answer 4

The only difference between Juan and Tom is the three extra days. They both paid the same fixed amount, and they both paid the daily charge up to 6 days. But then Tom kept his disk for three more days, and so he was charged more.



So the additional amount that Tom paid is because of those three days.



for 9 days = $27.00

for 6 days = $19.50

-----------------------------

for 3 days = $ 7.50



So for 3 extra days he paid $7.50 extra in fees.



Therefore, each day (after the first two) is $7.50 / 3 = $2.50



So for 10 days, the charge is 9 days @ $27.00 + 1 day @ $2.50 = $29.50 <--- answer



Check:



1) First find the fixed amount for the first two days

Juan paid for 4 additional days at $2.50 each, which is $10.00 in "daily" fees -- out of his $19.50 total.

So the fixed amount for the first two days is $9.50

So the rental company charges $9.50 for the first two days + $2.50 for each day thereafter



2) Second step: Test this to see if it produces the amount given for Tom

At 9 days, Tom paid

$9.50 as a fixed fee for the first two days

Plus $2.50 daily charge for 7 additional days, which is 7 * 2.50 = $17.50



$17.50 (daily charge)

+$9.50 (fixed fee)

------------

$27.00 Check

Answer 5

if you where to ask question with numbers instead of slang names of coins I may be able to help you