You have a jar containing 74 coins, consisting entirely of pennies and quarters, worth a total of $6.74. How many quarters are in the jar? Type in your numerical answer only; do not type any words or letters with your answer.
Accepted Solution
A:
Answer: 25Step-by-step explanation:We know that , 1 dollar = 100 penniesi.e. 1 penny = $ 0.011 dollar = 4 quarters i.e. 1 quarter = $ 0.25 Let x be the number of pennies and y be the number of quarters in the jar, then the system of equation represents the given situation will be :-[tex]x+y=74------(1)\\\\ 0.01x+0.25y=6.74------(2)[/tex]Multiply 100 on both sides of equation (2), we get [tex]x+25y=674-------(3)[/tex]Subtract (1) from (3), we get[tex]24y=600\\\\\Rightarrow\ y=\dfrac{600}{24}=25[/tex]Substitute y= 25 in equation (1), we get[tex]x+25=74\\\\\Rightarrow\ x=74-25=49[/tex]Hence, there are 49 pennies and 25 quarters in the jar.