Question

Samantha has some nickels and some jars. If she puts 4 nickels in each jar, she will have 1 empty jar leftover. If she puts 3 nickels in each jar, she will have 2 nickels left over. How many more nickels does Samantha have than jars?

Answer 1

Given :- Samantha has some nickels and some jars. If she puts 4 nickels in each jar, she will have 1 empty jar leftover. If she puts 3 nickels in each jar, she will have 2 nickels left over. How many more nickels does Samantha have than jars ?

Solution :-

Let us assume that, total nickels samantha has are N and total jars are J .

then, If she puts 4 nickels in each jar, she will have 1 empty jar leftover .

So, we can say that the number of jars is equal to the number of nickels divided by four plus another one.

• J = (N/4) + 1 .

Again, If she puts 3 nickels in each jar, she will have 2 nickels left over.

So, we can say that the number of nickels will be equal to the number of jars times three plus another one.

• N = 3J + 2 .

Solving both now , we get,

→ J = (3J + 2)/4 + 1

→ (J - 1) = (3J + 2)/4

→ 4J - 4 = 3J + 2

→ 4J - 3J = 2 + 4

→ J = 6 .

Then,

→ N = 3 * 6 + 2 = 18 + 2 = 20 .

Therefore,

→ More nickels does Samantha have than jars = 20 - 6 = 14 (Ans.)

Hence, Samantha have 14 more nickels than jars.

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