Let's denote:

• $q$ as the number of quarters.
• $d$ as the number of dimes.

We have two key pieces of information:

1. The total value of the coins is $5.35.
2. The total weight of the coins is 124 grams.

Step 1: Set up the equations

1. Value equation:

   • Each quarter is worth $0.25, and each dime is worth $0.10.
   • The total value is $5.35, so: $0.25q + 0.10d = 5.35$ Multiply through by 100 to eliminate decimals: $25q + 10d = 535$

2. Weight equation:

   • Each quarter weighs 6 grams, and each dime weighs 2 grams.
   • The total weight is 124 grams, so: $6q + 2d = 124$ Divide this equation by 2 to simplify: $3q + d = 62$

Step 2: Solve the system of equations

We now have the system of equations:

1. $25q + 10d = 535$
2. $3q + d = 62$

Solve the second equation for $d$:

$d = 62 - 3q$

Substitute this expression for $d$ into the first equation:

$25q + 10(62 - 3q) = 535$ Simplify: $25q + 620 - 30q = 535$ $-5q + 620 = 535$ $-5q = 535 - 620$ $-5q = -85$ $q = 17$

Find $d$ using $q = 17$:

$d = 62 - 3(17)$ $d = 62 - 51$ $d = 11$

Conclusion:

Jenny has 11 dimes.

Would you like more details or have any questions?

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Here are 5 related questions:

1. What if Jenny had $6.00 instead of $5.35?
2. How many coins in total does Jenny have?
3. What if the total weight was only 100 grams?
4. What if the quarters weighed 5 grams instead of 6 grams?
5. How much would the total value be if Jenny had 20 dimes?

Tip: Always check the units and ensure consistency when solving word problems involving money and weight!