SOLUTION: Use the 4 step process t answer this word problem: Assign and label variables, write a system of equations, solve the system, answer the question in a sentence.
In your coin p
Algebra ->
Customizable Word Problem Solvers
-> Coins
-> SOLUTION: Use the 4 step process t answer this word problem: Assign and label variables, write a system of equations, solve the system, answer the question in a sentence.
In your coin p
Log On
Question 1126934: Use the 4 step process t answer this word problem: Assign and label variables, write a system of equations, solve the system, answer the question in a sentence.
In your coin purse are dimes and quarters, 50 coins in all. The total value of the coins is $9.95. How many of each coin do you have?
Let D be the number of dimes and let Q be the number of quarters.
Then from the condition, you have this system of two equations in two unknowns
D + Q = 50 coins (1) (counting coins)
10D + 25Q = 995 cents (2) (counting cents)
From equation (1), express D = 50 - Q and substitute it into equation (2).
You will get a single equation for only one unknown Q (it is how the Substitution method works) :
10*(50-Q) + 25Q = 995.
Simplify and solve this equation for Q.
500 - 10Q + 25Q = 995,
15Q = 995 - 500
15Q = 495
Q = = 33.
Thus we found the unknown Q, which is the number of quarters.
Then from equation (1) you get D = 50 - Q = 50 - 33 = 17.
It is the value of dimes.
Answer. The collection has 17 dimes and 33 quarters.
Check. 17*10 + 33*25 = 995 cents. ! Correct !
The problem is solved and the answer is checked.
Done and completed.
----------------
It is good that the problem dictates us very stiff structure for the solution.
Now learn and memorize this solution as a mantra and repeat it EVERY TIME when you solve similar problems.
Notice that when listing the steps, the condition missed one critically important step: the solution MUST BE CHECKED at the end.
You will find there the lessons for all levels - from introductory to advanced,
and for all methods used - from one equation to two equations and even without equations.
Read them and become an expert in solution of coin problems.
