Answer:
a) 21 nickels and 2 dimes
b) [tex]5x+10y=125[/tex]
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 [tex]5x+10y[/tex] cents that is $1.25. Convert $1.25 into cents:
[tex]\$1.25=125\ cents,[/tex]
so the equation that describes the relationship between the number of dimes and number of nickels is
[tex]5x+10y=125[/tex]
a. To find one possible solution, substitute an arbitrary value of y and find x. Let y = 2, then
[tex]5x+10\cdot 2=125\\ \\5x+20=125\\ \\5x=125-20\\ \\5x=105\\ \\x=21[/tex]
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:
[tex]5\cdot 13+6\cdot 10=65+60=125[/tex]
True, so the point (13,6) a solution to the equation you wrote
