1. Ann has $300 made up of $5 and $10 bills. If there are 39 bills in all, how many $5 bills does she have? 2. A parking machine contained $3.05 made up of dimes and quarters. Ther... 1. Ann has $300 made up of $5 and $10 bills. If there are 39 bills in all, how many $5 bills does she have? 2. A parking machine contained $3.05 made up of dimes and quarters. There were 20 coins in all. How many dimes were there? 5. A professional soccer player is negotiating her contract. Using the advice of her manager, she asked for $80000 for the year, plus an additional $1500 for every game she plays in. The team offered $6000 for every game played and $600000 for the year. How many games would she need to play for the team’s offer to be the better option? 6. Supplying a sheep to a family costs AU$50 and a bee hive costs AU$35. If there were 24 gifts totaling AU$990, how many of each were bought? What would be the benefit of supplying a sheep or bee hive to a family? 8. Two social events have been organized by a local scout group to raise funds for a well in Tanzania. During the first night, 25 children and 20 adults attended and the revenue for that evening was £150. On the second night there were 30 children and 22 adults, with revenues of £170. How much did each adult pay to attend this social event, assuming that the ticket prices were the same for both events? 9. A basic Costco membership in the United States is $60 per year, while the premium membership is $120 per year. You get 2% back on Costco purchases with the premium membership and nothing back with the basic membership. How much money would you have to spend at Costco in a year before the premium membership is the better option for you to buy? 12. Find the equation of the line, in standard form, that passes through (-7, 3) and the point of intersection of 4x - y = 3 and 2x + y = 9.
Understand the Problem
The questions cover various mathematical problems including counting coins, financial negotiation, statistical analysis of events, cost analysis of items, and a linear equation problem. They require applying mathematical reasoning to find solutions for different scenarios.
Answer
There are 13 dimes and 7 quarters.
Answer for screen readers
The parking machine contains 13 dimes and 7 quarters.
Steps to Solve
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Understand the Coin Configuration
Given that the parking machine contains $3.05 made up of dimes and quarters, we will set up two equations. Let the number of dimes be $d$ and the number of quarters be $q$. We know:
$$ d + q = 20 $$
$$ 0.10d + 0.25q = 3.05 $$ -
Convert the Dollar Amounts to Cents
To eliminate decimals, multiply the second equation by 100:
$$ 10d + 25q = 305 $$ -
Substitute and Solve
Use the first equation to express $q$ in terms of $d$:
$$ q = 20 - d $$
Substitute into the second equation:
$$ 10d + 25(20 - d) = 305 $$
Expand and solve for $d$:
$$ 10d + 500 - 25d = 305 $$
$$ -15d + 500 = 305 $$
$$ -15d = 305 - 500 $$
$$ -15d = -195 $$
$$ d = 13 $$ -
Find the Number of Quarters
Substitute $d$ back into the first equation to find $q$:
$$ 13 + q = 20 $$
$$ q = 20 - 13 $$
$$ q = 7 $$ -
Conclusion of Values
Thus, there are 13 dimes and 7 quarters in the parking machine.
The parking machine contains 13 dimes and 7 quarters.
More Information
The problem illustrates the use of systems of equations to solve a real-world situation involving coin counts. This method can be applied to various similar problems where relationships need to be established.
Tips
- Not converting to the same units: Failing to convert dollar amounts to cents can complicate calculations.
- Incorrectly setting equations: Make sure to accurately frame the relationships as equations.
- Not substituting correctly: When substituting one equation into another, keep track of each variable carefully.
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