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Law Incorporation [45]
3 years ago
13

Luke invited 20 more boys than girls to his birthday party. However, only ¾ of the boys and ⅔ of the girls came. Exactly 19 of L

uke’s friends did not show up because they had to do some math homework. How many friends did he invite?
Mathematics
1 answer:
sveta [45]3 years ago
8 0

Answer:

68

Step-by-step explanation:

Let:

Number of girls invited = x

Number of boys = x +20

3/4 of boy showed up

2/3 of girls showed up

Exactly 19 did not show up

Therefore, we could say:

Fraction of boys that didn't show up = 1 - 3/4 = 1/4

Fraction of girls that didn't show up = 1 - 2/3 = 1/3

That is,

[1/4 *(x + 20)] + [1/3*x] = 19

[(x + 20) / 4] + x /3 = 19

(3(x + 20) + 4x) / 12 = 19

3x + 60 + 4x = 228

7x = 228 - 60

7x = 168

x = 168 / 7

x = 24

Number of girls, x = 24

Number of boys, x + 20 = 24 + 20 = 44

Total friends invited = (24 + 44) = 68

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Jon and Andy had a total of 560 trading cards. After Jon gave 1/9 of his trading cards to Andy, they has an equal number of trad
Romashka [77]

Answer:

70 cards

Step-by-step explanation:

Let A = the number of Andys cards

J = the number of Jons cards

Jon and Andy had a total of 560 trading cards

A+J = 560

After Jon gave 1/9 of his trading cards to Andy, they has an equal number of trading cards

J - 1/9 J = 1/9 J +A

Combine like terms

8/9 J = 1/9 J +A

Subtract 1/9J from each side

7/9J = A

Substitute this into A +J = 560

7/9J +J = 560

Combine like terms

7/9J +9/9J = 560

16/9 J = 560

Multiply each side by 9/16

9/16 *16/9 J = 560 *9/16

J =315

Jon originally had 315 cards

Now we need to find Andys cards

7/9J = A

7/9 (315) =A

245=A

How many more trading cards did Jon have that Andy in the beginning?

We need to take Jons cards and subtract Andys cards

J-A

315-245

70

6 0
4 years ago
2) Ten Percent of 27 is _<br> One Percent of 27 is<br> Find 14% of 27.
geniusboy [140]

Step-by-step explanation:

10%of 27

=  \frac{10}{100}  \times 27

=  \frac{27}{10}  = 2.7

1% of 27

=  \frac{1}{100}  \times 27 = 0.27

14\%of \: 27 =  \frac{14}{100}  \times 27 = 3.78

8 0
4 years ago
The square root of 1521 = 39, evequate 390 to the 2nd power
ki77a [65]

Answer:

390 to the second power is 152100

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3 years ago
Cathy recorded the percent of her clothing that is Red, Yellow, Blue, or Orange. The results are shown in the table. If Cathy ha
AleksandrR [38]
There are 145 total pieces . you must first convert 20% to a decimal by placing a decimal point two places from the right. 20% = .20
then you mulitiply 145 x .20 = 29
So, Cathy owns 29 pieces of yellow clothing.
7 0
4 years ago
Read 2 more answers
Toya can run one lap of the track in 1 min. 3 sec., which is 90% of her younger sister niki's time. what is niki's time for one
Alex
Hello!

1 minute 3 seconds = 63 seconds

We must found out 63 is 90% of what number, using the percentage formula:

90 * 100 / 63 = 70

70 seconds = 1 minute 10 seconds

So, Niki's time for one lap is 1 minute 10 seconds (70 seconds).
5 0
3 years ago
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