All categories

4 years ago

James and Jada together have $60. James has $9 more than twice Jada’s amount. How much money does each have?

Mathematics

1 answer:

sukhopar [10]4 years ago

7 0

Answer:

$43 and

$17

Step-by-step explanation:

Let the amount James have be A and that of jada be B

Given

James and jada have $60 together

That’s

A + B = 60

And james A has $9 more than twice jada’s amount

That’s

A = 9 + 2B

We now have two equations

1. A + B = 60 and

2. A = 9 + 2B

Now put 9 + 2B as A in equation one

A + B = 60

9 +2B + B = 60

9 + 3B = 60

Subtract 9 from both sides

9 - 9 + 3B = 60 - 9

3B = 51

Divide both sides by 3

3B/3 = 51/3

B = 17

Jada has $17

Recall

A = 9 + 2B

And B = 17

Therefore

A = 9 + 2 x 17

A = 9 + 34

A = 43

James has $43

Therefore, James has $43 while jada has $17

You might be interested in

4. a) A ping pong ball has a 75% rebound ratio. When you drop it from a height of k feet, it bounces and bounces endlessly. If t

Klio2033 [76]

First part of question:

Find the general term that represents the situation in terms of k.

The general term for geometric series is:

$a_{n}=a_{1}r^{n-1}$

$a_{1}$ = the first term of the series

$r$ = the geometric ratio

$a_{1}$ would represent the height at which the ball is first dropped. Therefore:

$a_{1} = k$

We also know that the ball has a rebound ratio of 75%, meaning that the ball only bounces 75% of its original height every time it bounces. This appears to be our geometric ratio. Therefore:

$r=\frac{3}{4}$

Our general term would be:

$a_{n}=a_{1}r^{n-1}$

$a_{n}=k(\frac{3}{4}) ^{n-1}$

Second part of question:

If the ball dropped from a height of 235ft, determine the highest height achieved by the ball after six bounces.

$k$ represents the initial height:

$k = 235\ ft$

$n$ represents the number of times the ball bounces:

$n = 6$

Plugging this back into our general term of the geometric series:

$a_{n}=k(\frac{3}{4}) ^{n-1}$

$a_{n}=235(\frac{3}{4}) ^{6-1}$

$a_{n}=235(\frac{3}{4}) ^{5}$

$a_{n}=55.8\ ft$

$a_{n}$ represents the highest height of the ball after 6 bounces.

Third part of question:

If the ball dropped from a height of 235ft, find the total distance traveled by the ball when it strikes the ground for the 12th time. 

This would be easier to solve if we have a general term for the <em>sum </em>of a geometric series, which is:

$S_{n}=\frac{a_{1}(1-r^{n})}{1-r}$

We already know these variables:

$a_{1}= k = 235\ ft$

$r=\frac{3}{4}$

$n = 12$

Therefore:

$S_{n}=\frac{(235)(1-\frac{3}{4} ^{12})}{1-\frac{3}{4} }$

$S_{n}=\frac{(235)(1-\frac{3}{4} ^{12})}{\frac{1}{4} }$

$S_{n}=(4)(235)(1-\frac{3}{4} ^{12})$

$S_{n}=910.22\ ft$

8 0

3 years ago

A Man is redecorating his bedroom .he can choose from 5 paint colors 6 beds and 5 dressers how many ways can he choose to design

Ipatiy [6.2K]

$5_{(paint\ colors)}\ \cdot\ 6_{(beds)} \ \cdot\ 5_{(dressers)}=150_{(chooses)} \\\\Ans.\ 150\ chooses.$

8 0

3 years ago

Read 2 more answers

Adriana va a llenar bolsas de dulces para su fiesta de cumpleanos si tiene un paquete con 100 paletas y otro con 56 chocolates y

lions [1.4K]

Answer:

56 bags of a chocolate and a popsicle

Step-by-step explanation:

The first thing is to find the relationship between the number of popsicles and the number of chocolates, which would be the quotient of these:

100/56 = 1.78

Since it does not reach number two, you cannot add 2 popsicles and 2 chocolates, therefore the only way that they contain the same amount is that there is a chocolate and a popsicle, that is to say that a total of 56 bags would come out.

6 0

3 years ago

Question 8 The product of – x2 + 5x – 1 and a monomial is 4x2 20x + 4. What is the monomial? ОА 4. B 4X С -4 -47

Scrat [10]

Answer: -4

Step-by-step:

-x^2+5x-1 x _ = 4x^2-20x+4

4x^2-20x+4 / -x^2+5x-1

In the blank the answer would be -4 which is the monomial.

6 0

3 years ago

The Large square represents one whole.<br> 3.74 - 1.53 = ?

qwelly [4]

Answer:

2.21

Step-by-step explanation:

4 0

3 years ago