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# Questions

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Here is a list of questions:

Peter and Cindy each had some money at first. Peter started spending \$1.20 daily.

After 15 days, Cindy started spending 1 2/3 of what Peter spent daily. When CIndy
spent all of her money, she had spent \$11.60 more than Peter.

a) How many days did Cindy take to spend all of her money?
b) How much did Peter spend in total when Cindy spent all of her money?

An organisation provides packets of food daily for needy residents living in three blocks of flats. Block 1 receives 1/5 of the packets of food. Block 2 receives 175 more packets of food than Block 1. Block 3 receives 75 more packets of food than Block 1. How many packets of food does the organisation provide daily?

Jillian has \$2,000 in credit card debt. Every month, she pays \$200 to the credit card company at the beginning of the month, the credit card company applies a 2% monthly interest rate to the balance at the end of the month, and her balance is always rounded to the nearest cent. After the end of five months, what is her ending balance after interest?

Bart had \$635 and Ernie had \$403. After they shared the cost of a present equally. Ernie had 3/5 the amounted money Bart had. How much did each of them pay for the present?

Jul 27, 2023

#1
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Two more questions:

In October, Jeremy spent \$390 on food which was 1/3 of his salary. He gave his parents 4/9 of his salary. He spent half of the remaining money on transport and saved the other half. How much money did he save?

Shayden had \$243. He spent 2/9 of his money to buy 5 chocolate bars and 6 packets of potato chips. The cost of 3 packets of potato chips was the same as the cost of 2 chocolate bars. Find the greatest number of chocolate bars that he could buy with the money he had left.

Jul 27, 2023
#2
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First question:

C==Cindy,   D==Number of days it took her to spend her money

15 * \$1.20 ==\$18 - what Peter spent in 15 days.

5/3 * \$1.20==\$2 - what Cindy spent daily

C/\$2 ==D.............................................(1) - Number of days it took Cindy to spend all her money

\$18 + \$1.20D + \$11.60 =2D................(2), solve for C, D

D==37 days it took Cindy to spend all her money

37 * \$2 ==\$74 - total amount that Cindy spent

\$18 + {\$1.20 * 37 days)==\$18 + \$44.40 =\$62.40 - total amount spent by Peter.

Check: \$74 - \$62.40 ==\$11.60 extra amount spend by Cindy over Peter.

Jul 27, 2023
#12
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Nice Job!

history  Jul 27, 2023
#3
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2nd question:

P==Packets of food

1/5P - packets distributed to Block 1

1/5P + 175 - packets distributed to Block 2

1/5P + 75 - packets distribted to Block 3

1/5P + [1/5P + 175] + [1/5P + 75] = P, solve for P

P==625 -  packets of food disributed daily

Jul 27, 2023
#11
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Nice!

history  Jul 27, 2023
#4
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4th question:

Let the cost of the present==P

635 - P/2==what Bart had left after paying the present.

403 - P/2==what Ernie had left after after paying for the present

403 - P/2 ==3/5 [635 - P/2], solve for P

P==\$110 - cost of the present

\$110 / 2 ==\$55.00 - what each paid for the present.

Jul 27, 2023
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Excellent!

history  Jul 27, 2023
#5
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I will solve the first question

a.

Daily spending by Peter = \$1.20

Daily spending by Cindy = 1 2/3 of Peter's daily spending = \$1.20 * 1 2/3 = \$1.20 * 5/3 = \$2.00

Cindy started spending 15 days after Peter started. When Cindy spent all of her money, she had spent \$11.60 more than Peter.

Let 'n' be the number of days takes Cindy to spend all the money. Therefore

Cindy's total spending -- \$11.60 = Peter's total spending

(\$2.00 * n) + \$11.60 = \$1.20 * (n + 15)

2n - 11.60 = 1.20n + 18

0.80n = 29.60

n = 29.60/0.80

n = 37

b.

Number of days taken by Peter = Number of days taken by Cindy to spend all money + 15 = 37 + 15 = 52 days

The total spending of Peter when Cindy had spent all the money is

Total spending = Number of days * Daily spending = \$52 * \$1.20 = \$62.40

a. Cindy took 37 days to spend all of her money.

b. Peter had spent \$62.40 in total when Cindy spent all of her money.

It's not that hard :)

Jul 27, 2023
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Nice work!

history  Jul 27, 2023
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5.

1/3 part of salary = \$390

Total salary = \$390*3/1 = \$1170

Amount given to parents = \$1170*4/9 = \$520

Remaining money = Total salary - Spending on food - Amount given to parents

= \$1170 - \$390 - \$520 = \$260

Amount saved = 1/2 of remaining money

= \$260*1/2 = \$130

Money saved = \$130

6.

Let, the cost of each chocolate bar = x

Cost of each pack of potato chips = y

so,

=> 5x + 6y = 2/9 * 243

=> 5x +6y =54............(i)

and,

=> 3y = 2x

=> y = 2/3x................(ii)

Substituting value of y in (i):
=> 5x + 6(2/3x) = 54

=> 5x + 4x = 54

=> 9x = 54

=> x = 54/9

=> x = 6

Substituting value of x in (ii):

=> y = 2/3(6)

=> y = 4

So,

Cost of each chocolate bar = \$6

Cost of each pack of potato chips = \$4

Amount of money left = (1 - 2/9) * 243 = 7/9 * 243 = \$189

Finding greatest number of chocolate bars he cay buy:
=> 189/6

=> 31.5

so,

Greatest number of chocolate bars he cay buy = 31

Jul 27, 2023
#8
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Nice Job!

history  Jul 27, 2023
#7
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One more question :)

Tobias brought some money out for shopping to prepare for his backpack travelling this December. He spent 3/7 of his money on a backpack and 2/3 of the remaining amount of money on 3 identical purification bottles. He spent the rest of his money on 3 travel first aid kits. The cost of a purification bottle is \$14.80 more than the cost of each first aid kit. How much money did Tobias spend on the backpack and purification bottles altogether?

Jul 27, 2023
#13
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I think I seen this problem

Let total money of Tobias is \$x

He spent amount of money in backpack is

\$3x/7

Remaining amount = \$(x - 3x/7) = \$4x/7

Total money spent on 3 purification bottles is \$(4x/7 * 2/3) = \$8x/21

Remaining amount = \$(4x/7 - 8x/21)

= \$((12x - 8x))/21)

= \$4x/21

Cost of 3 first aid kits = \$4x/21

Cost of each first aid kits = \$(4x/21 / 3)

= \$4x/63

Cost of each purification bottles = \$(8x/21 / 3)

= \$8x/63

According to our problem

8x/63 - 4x/63 = 14.80

=> 4x/63 = 14.80

=> 4x = (14.80) (63)

=> x = ((14.80) (63))/4

=> x = 233.10

The amount of money spent on backpack

= \$ (3/7 * 233.10)

= \$ 99.90

Remaining amount = \$(233.10 - 99.90)

= \$133.20

The amount of money spent on purification bottles = \$(2/3 * 133.20)

= \$88.80

Thus the total amount of money spent on backpack and purification bottles is \$(99.90 + 88.80) = \$188.70

The total amount of money spent on backpack and purification bottles is \$188.70

jhazerybrown2  Jul 27, 2023
#14
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Nice

Jul 27, 2023