#21 on my homework...need help!?

Question

Mrs. Rinaldo changed a $100 bill in a bank. She received $30 bills and $10 bills. The number of $20 bills was 2 more than the number of $10 bills. How many bills of each kind did she receive?

Please help me step by step to solve. Let statement is needed.

it's not $30 bills, it's $20 bills. so the statement should say "She received $20 bills and $10 bills."

Answer 1

your starting equation is 20(x+2)+10x=100
1) remove parenthesis by using distributive property
20x+40+10x=100
2) combine like terms, if any
20x+10x+40=100
30x+40=100
3) subtract 40 form both sides to isolate the variable
30x+40-40=100-40
4) the plus 40 and the minus 40 cancel each other out, leaving...
30x=100-40
5)subtract 100-40
30x=60
6) divide each side by 30 to isolate the variable
x=2.

Remember, X represents the number of 10 dollar bills. x+2 represents the number of 20 dollar bills. to find the number of 20 dollar bills you need to do 2+2=4.

So, she got 2 ten dollar bills and 4 twenty dollar bills.

(I'm not sure what a let statement is, buti'm sure you can figure it out with this!)

Answer 2

to answer this question list out all the possibilities of $10 and $20 combinations that add up to $100

so:
2 $10 and 4 $20 would make $100
4 $10 and 3 $20
6 $10 and 2 $20
8 $10 and 1 $20

then figure out which combination has 2 $20 bills more than $10.
and it's the first one!

answer: 2 $10 bills and 4 $20 bills.

Answer 3

let a be the number of $10 bills
and b be the number of $20 bills.

b = a + 2
10a + 20b = 100

10a + 20(a+2) = 100
10a + 20a + 40 = 100
30a = 60
a = 2

b = a + 2
b = 2 + 2
b = 4

so she recieved 2 $10-bills and 4 $20-bills

Answer 4

she recieved 4 20's and 2 10's. 4 times 20 is 80. 10 times 2 is 20. 20 + 80 = 100.