Each tray has 5 colours and one of the colour on the tray is purple. Hence 1/5 of the colours on the tray is purple and thus 1/5 of the colours on the 20 trays is purple. The fraction of colours on the trays will not change. If written out logically, 20 purples out of 100 colours in total on the trays will also given the fraction 1/5.

4 0

3 years ago

9. Simran had some ₹2 and ₹ 5 coins.She exchanged them for ₹ 10 coins. If the number of ₹ 5 coins is one less than the number of

sertanlavr [38]

Answer:

Step-by-step explanation:

Let x be the number of 2 coins and y be the number of 5 coins. Let z be the number of 10 coins she exchanged. Then, we have the first equation

$2x+5y = 10z$

Since she has one 5 coin less than 2 coins, then y=x-1. So we get the equation

$2x+5(x-1) = 10z$

which is equivalent to

$7x-5 = 10z$

If we add 5 on both sides and factor out on the right by 5 we get

$7x = 5(2z+1)$

We can solve for x and get

$x = \frac{5(2z+1)}{7}$

Since x represents the number of 2 coins, we must have that x is an integer. That is, we cannot have, for example 1.5 2 coins. Since 7 doesn't divide 5, we must have that 7 divides 2z+1. That is, the value of z is such that the number 2z+1 is multiple of 7. That is 2z+1 = 7p where p is an integer.

If that is the case, then

x = 5p, then y = 5p-1. By having 2z+1 = 7p, we are forcing that p is an odd integer, so we have infinite solutions. For each value of p that is an odd integer, then x=5p and y=5p-1 is a solution to the problem

7 0

4 years ago