A charity organization is collecting change to raise money. They have collected three times as many dimes as quarters, 11 more nickels than dimes, and 2 times as many pennies as nickels. Let x represent the number of quarters. Write an expression to represent the number of dimes. Write an expression to represent the number of nickels. Write an expression to represent the number of pennies. If they have collected a total of 4,453 coins, how many of each coin have they collected? Show your work.

x = no. of quarters

3x = no. of dimes

3x + 11 = no. of nickels

2(3x + 11) = no. of pennies

340 quarters

1020 dimes

1031 nickels

2062 pennies

Step-by-step explanation:

x = no. of quarters

3x = no. of dimes

3x + 11 = no. of nickels

2(3x + 11) = no. of pennies

x + 3x + 3x + 11 + 2(3x + 11) = 4453

x + 3x + 3x + 11 + 6x + 22 = 4453

13x + 33 = 4453

13x = 4420

x = 340 quarters

3x = 1020 dimes

3x + 11 = 1031 nickels

2(3x + 11) = 2062 pennies

Check:  340 + 1020 + 1031 + 2062  = 4453

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.