smart math peoples heres a question?

Question

the coins represent a quarter, a dime, and a nickel. A quarter weighs 6 grams, a dime weighs 2 grams, and a nickel weighs 5 grams.What combination of coins would weigh 30 grams and have a combined value of 1 dollar? the answer: 2 nickels, 2 quarters and 4 dimes now here's the question if a penny weighs 1/5 of a gram, which coin could be replaced with the penny? explain work.

Answer 1

set up a systems of equations. let quarter = q, dime = d, and nickel = n

so, value can be determined as:

V= 2.5q + .10d + .05n = 1.00

and mass [in grams] can be determined as:

M = 6q + 2d + 5n = 30

this means:
2.5q + .10d + .05n = 1.00
6q + 2d + 5n = 30

Solve. by yourself. good practice.

Answer 2

since a dime weighs 2 grams and a penny 1/5 of a gram then as far as mass goes 10 pennies equals a dime. as far as money goes 10 pennies also equal one dime. this would not work for any of the other coins.


i guess if you want to make it look cool

1 penny = 1/10 dime 1/25 nickle 1/30 quarter mass wise
1 penny = 1/10 dime 1/5 nickle 1/ 25 quarter monetarily

since monetary and mass would be an equal substitution then dime is the only one that would work.

Answer 3

Either or both of the dimes could then be replaced with pennies because 1 gram of pennies would equal 5 cents and 2 grams would equal 10 cents, equivalent to a dime.

Answer 4

It would be the dime because there are four dimes, each weighing 2 grams. 4*2=8 grams and 40 pennies would weigh 8 grams.

Answer 5

first try dimes, nickels and pennies
i: 10D + 5N + P = 100
ii: 2D + 5N +.2P = 30
subtract i from 5ii
20N = 50 no integral solution

now try quarters, dimes, and pennies
25Q+10D+P = 100
6Q+2D+.2P = 40
again, subtract i from 5ii
5Q = 100 Q=20 more than $1. no good

now try quarters, nickels, and pennies
i: 25Q + 5N + P = 100
ii: 6Q + 5N + .2P = 30
again, subtract i from 5ii
5Q + 20N = 50 or Q + 4N = 10
only possible solution is Q=N=2, where P=40
$1, 30 grams

Answer 6

looks like 2 nickels.

Answer 7

dime