Respuesta :
Answer:
The numbers of red marbles does Pam have is 29 .
Step-by-step explanation:
Given as :
The total number of marbles including red marbles and black marbles does Pam has = 42
Let The number of red marbles which Pam has = R
And The number of black marbles which Pam has = B
So, The total number of marbles = The number of red marbles + The number of black marbles
I.e R + B = 42 .........1
According to question
The number of red marbles she has is three more than twice the number of black marbles she has .
I.e R = 3 + twice of B
Or , R = 3 + 2 × B .........2
Now, solving Eq 1 and 2
Put The value of R from eq 2 into eq 1
So, ( 3 + 2 × B ) + B = 42
or, 3 + 2 B + B = 42
Or, 3 B = 42- 3
Or, 3 B = 39
∴ B = [tex]\frac{39}{3}[/tex]
I.e B = 13
Now, put the value of B in eq 2 , we get
R = 3 + 2 × B
Or, R = 3 + 2 × 13
∴ R = 3 + 26
I.e R = 29
So, Number of black marbles does Pam have = B = 13
And Number of red marbles does Pam have = R = 29
Hence The numbers of red marbles does Pam have is 29 . Answer
You can use variables to denote the amount of each marble and then use the given description to find the amount of marbles Pam has got.
The amount of red marbles Pam have is 29
How to form mathematical expression from the given description?
You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.
How many red marbles does Pam have?
To find that, let we first suppose the amount of each marble.
]Suppose Pam has got [tex]x[/tex] red marbles
and has got [tex]y[/tex] black marbles.
Since it is given that she has got, in total, 42 marbles, thus,
[tex]x + y = 42\\[/tex]
It is said that the number of red marbles is three more than twice the number of black marbles.
This can be stated as [tex]x = 3 + 2 \times y[/tex]
(remember that many times, when using letters or symbols, we hide multiplication and write two things which are multiplied, close to each other. As in [tex]2 \times y = 2y[/tex] )
Putting this expression for [tex]x[/tex] in first equation, we get
[tex]x + y = 42\\\\3 + 2y + y = 42\\3 + 3y = 42\\\\\text{Subtracting 3 from both the sides}\\3 + 3y - 3 = 42 - 3\\3y = 39\\\\\text{Dividing both the sides by 3}\\\\\dfrac{3y}{3} = \dfrac{39}{3}\\\\y = 13[/tex]
Putting this value of y in x + y = 42
[tex]x + y = 42\\x + 13 = 42\\\\\text{Subtracting 13 from both the sides}\\\\x = 29[/tex]
Thus, Pam has got x red marbles= 29 red marbles and y black marbles= 13 black marbles.
Learn more about system of equations here:
https://brainly.com/question/13722693
