Question

Rekha collected some coins of Rs 1 rupees and 5 rupees in her Piggy Bank if we had 320 in total and total numbers of coins where 200 find the number of coins of each denomination​

Answer 1

Answer:

170; 1 rupee coins , 30; 5 rupee coins

Step-by-step explanation:

given

piggy bank has 1 and 5 rupee coins

total amount in piggy bank = 320

total no of coins = 200

to find

no of 1 rupee coins

no of 5 rupee coins

assumptions

lets assume that number of 1 rupee coins in piggy bank are x

lets assume that number of 5 rupee coins in piggy bank are y

solution

total no of coins = x + y

                           = 200

equation 1      ------>  x + y =200

total amount in piggy bank is 320

                                                = 1 × x + 5 × y

                                                = x + 5y

equation 2 -------->   x + 5y = 320

solving

eq 1,eq2

x + y =200

x + 5y = 320

==> 4y = 120

==> y = 30

==>x + 30 = 200                   from eq 1

===> x =170

therefore number of 1 rupee coins = 170

                number of 5 rupee coins = 30

Answer 2

Let's the number of 1 rupee coins be x.

And the number of 5 rupee coins be y.

And the number of 1 rupee coins and 5 rupee coins combine together to get 200 coins.

So, let's write the above situation arithmetically, or put it in an equation;

x + y = 200

And let's term the above equation as Equation 1.

And we can have one more equation, i.e., x + 5y = 320;

**How?? As we know that the total amount is ₹320, so the number of 1 rupee coins and the number of 5 rupee coins together is ₹320**

**Why 5y?? That's because y is just the number of coins, so we have to multiply 5 with it so that it becomes the amount of  5 rupee coins**

So, now let's term the above equation as Equation 2.

Now let's start solving the question;

First let's try to find the value of y using elimination;

So, by subtracting Equation 1 from Equation 2, we get;

4y = 120

As we have to isolate y, let's divide the equation by 4;

$\dfrac{\cancel{4}\text{y}}{\cancel{4}}=\dfrac{120}{4}$

Simplify;

y = 30

Now, let's substitute the value of y to equation 1, to find the value of x;

x + (30) = 200

Subtract 30 from both the sides;

x + 30 - 30 = 200 - 30

Simplify;

x = 170

Therefore, there are 170 coins of 1 rupee and 30 coins of 5 rupee.