We have a jar of coins, all pennies and quarters. All together, we have 302 coins, and the total value of all coins in the jar is $ 42.86. How many pennies are there in the jar?

There are 136 pennies in the jar

Step-by-step explanation:

The expression for the total value of money Aria has is;

Penny has a value of = $0.01

Quarter has a value of = $0.25

Total value = (value of a quarter*number of quarters) + (value of a penny*number of pennies)

where;

Total value=$42.86

Value of a quarter=$0.25

number of quarters=x

Value of a penny=0.01

number of pennies=y

replacing;

42.86 = (0.25*x) + (0.01*y)

0.25 x+0.01 y=42.86 ... equation 1

The total number of coins=number of quarters+number of pennies

where;

Number of quarters=x

Number of pennies=y

Total number of coins=302

replacing;

x+y=302 ... equation 2

Combine equation 1 and 2 and solve simultaneously;

1 (x+y=302) 1

-

4 (0.25 x+0.01 y=42.86)

x-4 (0.25 x) + y - (0.01 y*4) = 302 - (4*42.86)

0+0.96 y=130.56

0.96 y=130.56

y=130.56/0.96

y=136

Replace the value of y in equation 2

x+136=302

x=302-136

x=166

Number of quarters=x=166

Number of pennies=y=136