Question

Barney has a bag of $1 and $2 coins. the total mass of the coins is 71.4 grams. Barney knows that: the mass of a $1 coin is 9 grams and the mass of a $2 coin is 6.6 grams. what is the smallest mass of exactly $3 worth of coins?

Answer 1

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

Solution:

Step 1: Set up a table with quantity and value.

quantity value total

nickels

quarters

together

Step 2: Fill in the table with information from the question.

Jane bought a pencil and received change for $3 in 20 coins, all nickels and quarters.

Let n = number of nickels

q = number of quarters

Total = quantity × value

quantity value total

nickels n 5¢ 5n

quarters q 25¢ 25q

together 20 300¢

Step 3: Add down each column to get the equations

n + q = 20 (equation 1)

5n + 25q = 300 (equation 2)

Use Substitution Method

Isolate variable n in equation 1

n = 20 – q (equation 3)

Substitute equation 3 into equation 2

5(20 – q) + 25q = 300

100 – 5q + 25q = 300

25q – 5q = 300 – 100

20q = 200

q = 10

Substitute q = 10 into equation 1

n + 10 = 20

n = 10