Question

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

$1.25. (From Unit 2, Lesson 5.)

ch of nickels and dimes in her pocket and that the total amount is

a. Find one possibility for the number of nickels and number of dimes that could

pocket

b.

Write an equation that describes the relationship between the number of dimes and me

number of nickels in Priya's pocket.

c.

Explain what the point (13,6) means in this situation.

d.

Is the point (13,6) a solution to the equation you wrote? Explain your reasoning.

Answer 1

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

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