Two math problems

1) The sum of twice a number and -6 is nine more than the opposite of that number. Find the number.

2) A collection of 27 coins, all nickels, and dimes, is worth $2.10. How many of each coin are there? The dime, in United States usage, is a ten-cent coin. A nickel, in American usage, is a five-cent coin composed of 75% copper and 25% nickel.

Correct answer:

a =  5
d =  15
n =  12

Step-by-step explanation:

2a+(-6) = 9 + (-a)

2•a+(-6) = 9 + (-a)

3a = 15

a = 5

Our simple equation calculator calculates it.

d + n = 27
0.10d + 0.05n = 2.10

d + n = 27
0.10•d + 0.05•n = 2.10

d+n = 27
0.1d+0.05n = 2.1

d = 15
n = 12

Our linear equations calculator calculates it.

Try another example

Related math problems and questions:

• Banknotes
  $ 1390 was collected. How much was in $20 notes and how many in $50 notes in that order? How many solutions exists?
• Bronze, tin and copper
  Bronze is an alloy of tin and copper. An alloy of 10% tin and 90% copper is Gunmetal. If it contains 20% tin and 80% copper, it is bell metal. How many tons of molten bell metal and how many tons of copper is needed to make 100 tons of Gunmetal?
• Solutions, mixtures
  We have 2 liters of 20% solution available. How much 70% solution do we need to add to it to get a 30% solution?
• A man 2
  A man divides $10,000 into two investments, one at 10% and the other at 30%. Find how much is invested at each rate so that the two investments produce the same income annually.
• Alcohol 2
  Two types of alcohol one 63% and second 75% give 20 liters of 69% alcohol. How many liters of each type are in the mixture?
• Czech coins
  John has 540 CZK, but he has 10 CZK coins and 20 CZK coins only, we knows that he has 10CZK coins 7times more that 20CZK coins, how many 10CZK coin and how many 20CZK coins he saved?
• Sum of three numbers
  The sum of three numbers from which second number is 20% smaller than the first number and the third number is 25% smaller than the second number is 96. Determine this numbers.
• The number 72
  The number 72 increase by 25%. By how much % will you have to reduce the number you created to get the number 72 again?
• Four numbers
  The first number is 50% second, the second number is 40% third, the third number is 20% of the fourth. The sum is 396. What are the numbers?
• Coins
  The money - coins are minted from the hardest bronze, which contains copper and tin in a ratio of 41: 9. How much copper and tin are in 2kg of bronze money?
• Coins
  In the ticket machine were together one hundred coins. They were only 20 and 50 cent coins. The sum total was 29 euros and 60 cents. How many were in ticket machine coins, and which type?
• Four pupils
  Four pupils divided $ 1485 so that the second received 50% less than the first, the third 1/2 less than a fourth, and fourth $ 154 less than the first. How much money had each of them?
• Mixture 2
  How many liters of water must be added to 7 liters of a 20% solution to obtain a 10% solution?
• Sales of products
  For 80 pieces of two quality products a total sales is 175 Eur. If the first quality product was sold for n EUR per piece (n natural number) and the second quality product after 2 EUR per piece. How many pieces of the first quality were sold?
• Solutions, mixtures
  How many liters of 70% solution we must add to 5 liters of 30% solution to give us a 60% solution?
• Saving 9
  An amount of $ 2000 is invested at an interest of 5% per month. If $ 200 is added at the beginning of each successive month but no withdrawals. Give an expression for the value accumulated after n months. After how many months will the amount has accumula
• Czech crowns
  Oldrich has one crown. Peter has five crowns coin, a two crown coin and a one-crown coin. Radek has twenty-crown banknote, ten banknote and five-crown coin. The boys got one fifty-one crown and one crown coin. How can they share the money fairly when they