Coins...1

[nycmathguy]

I am interested in the set up only. Thanks.

1. Jane bought a pencil and received change for $3 in 20 coins, all nickels and quarters. How many of each kind are given?

Let n = nickels

Let q = quarters

A nickel = 0.05.

A quarter = 0.25

n + q = 20
0.05n + 0.25q = 3.00

Correct?

2. John received change worth $13. He received 10 more dimes than nickels and 22 more quarters than dimes. How many coins of each did he receive?

Let d = dimes

Let q = quarters

Let n = nickels

10 + d = n

q = 22 + d

0.05(10 + d) + 0.25(22 + d) = 13.00

You say?


3. Barb has $1.15 in her wallet, which contains 18 coins in nickels and dimes. Find how many of each kind coin she has in her wallet.

Let n = nickels
Let d = dimes

My first equation is n + d = 18.

Mty second equation is 0.05n + 0.10d = 13.00

You say?

 

[MathLover1]

1. correct set up
2. incorrect
you di not use dimes at all: 0.05(10 + d) + 0.25(22 + d) = 13.00=> you have only nickels and quarters expressed in terms of dimes

try this way:
n, d, and q are the number of nickels, dimes, and quarters. The 5, 10, and 25 are their value in cents.

5n + 10d + 25q = 1300

Put everything in terms of n: given d=n+10 and q=d+22=(n+10)+22 =n+32

5n + 10(n + 10) + 25(n + 32) = 1300

Expand everything:

5n + 10n + 100 + 25n + 250 + 550 = 1300

Group into like terms, and subtract the constants from both sides:

40n = 400

Finally, divide both sides by 40:

n = 10

d = n + 10 = 20

q = n + 32 = 42

42 quarters, 20 dimes, and 10 nickels


3.
n + d = 18.......correct

second equation is 0.05n + 0.10d = 13.00-> incorrect, Barb has $1.15 in her wallet

so, it should be 0.05n + 0.10d =1.15

 

[nycmathguy]

1. correct set up
2. incorrect
you di not use dimes at all: 0.05(10 + d) + 0.25(22 + d) = 13.00=> you have only nickels and quarters expressed in terms of dimes

try this way:
n, d, and q are the number of nickels, dimes, and quarters. The 5, 10, and 25 are their value in cents.

5n + 10d + 25q = 1300

Put everything in terms of n: given d=n+10 and q=d+22=(n+10)+22 =n+32

5n + 10(n + 10) + 25(n + 32) = 1300

Expand everything:

5n + 10n + 100 + 25n + 250 + 550 = 1300

Group into like terms, and subtract the constants from both sides:

40n = 400

Finally, divide both sides by 40:

n = 10

d = n + 10 = 20

q = n + 32 = 42

42 quarters, 20 dimes, and 10 nickels


3.
n + d = 18.......correct

second equation is 0.05n + 0.10d = 13.00-> incorrect, Barb has $1.15 in her wallet

so, it should be 0.05n + 0.10d =1.15

Thank you.