Question

Clare knows that Priya has a bunch of nickels and dimes in her pocket and that

Answer 1

Answer:

a) 21 nickels and 2 dimes

b) $5x+10y=125$

c) There are 13 nickels and 6 dimes

d) The point (13,6) a solution to the equation you wrote

Step-by-step explanation:

Let x be the number of nickels and y be the number of dimes in Priya's pocket.

1 nickel = 5 cents

x nickels = 5x cents

1 dime = 10 cents

y dimes = 10y cents

b. Total amount in nickels and dimes is $5x+10y$ cents that is $1.25. Convert $1.25 into cents:

$\ 1.25=125\ cents,$

so the equation that describes the relationship between the number of dimes and number of nickels is

$5x+10y=125$

a. To find one possible solution, substitute an arbitrary value of y and find x. Let y = 2, then

$5x+10\cdot 2=125\\ \\5x+20=125\\ \\5x=125-20\\ \\5x=105\\ \\x=21$

21 nickels and 2 dimes

c. The point (13,6) means that there are 13 nickels and 6 dimes.

d. Substitute x = 13 and y = 6 intoe the equation and check whether it is true:

$5\cdot 13+6\cdot 10=65+60=125$

True, so the point (13,6) a solution to the equation you wrote