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oee [108]
3 years ago
9

A group of students planned to chip in to raise a total of $100 for one of their friends’ birthday party but 5 persons couldn’t

come so they didn’t pay. This increased the share of the others by $1 each. Find the amount that each person paid after
Mathematics
1 answer:
lilavasa [31]3 years ago
8 0

Answer:

$5

Step-by-step explanation:

Let the number of students be x, then

<u>Initial amount per student was:</u>

  • 100/x

<u>After it becomes:</u>

  • 100/(x - 5)

<u>Since amount increased after, it can be shown as:</u>

  • 100/x + 1 = 100/(x - 5)

<u>Multiply each term by x(x - 5) to get rid of the fraction:</u>

  • 100(x-5) + x(x - 5) = 100x
  • 100x - 500 + x² - 5x - 100x = 0
  • x² - 5x - 500 = 0

<u>Positive solution of this quadratic equation is </u>

  • x = 25

<u>Amount each person paid after:</u>

  • $100 / (25 - 5) = $5

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Hayley has $155 in savings, and her brother Hank has $230. Hayley is saving $10 each week, and her brother is spending $15 each
Sindrei [870]

Answer:

After 3 weeks they both will have the same amount in their savings account.

Step-by-step explanation:

Given:

Amount saved by Haley = $155

Amount saved by Hank = $230

Amount saving each week by Haley = $10

Amount spending each week by Hank = $15

We need to find Number of weeks when both both will have same amount in savings account.

Solution:

Let Number of week be 'x'.

Total Amount of Haley can be calculated by Amount saved by Haley plus Amount saving each week by Haley multiplied by number of weeks.

framing in equation form we get;

Total Amount of Haley = 155+10x

Also;

Total Amount of Hank can be calculated by Amount saved by Hank minus Amount spending each week by Hank multiplied by number of weeks.

framing in equation form we get;

Total Amount of Hank = 230-15x

Now we need to find the number of weeks when both will have same amount.

To find the same we will have to make both the equation equal.

So we can say.

155+10x=230-15x

On Solving above equation we get;

We will combine the like terms together;

10x+15x =230-155\\\\25x = 75

Now Dividing both side by 25 using Division property of equality we get;

\frac{25x}{25} = \frac{75}{25}\\\\x=3 \ weeks

Hence, After 3 weeks they both will have the same amount in their savings account.

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