Category: Algebra
"Published in Vacaville, California, USA"
The sum of two numbers is twice their difference. The larger number is 6 more than twice the smaller. Find the numbers.
Solution:
From the description of a given word problem, it is an application of linear equation with one variable.
Let x = be the value of a smaller number
2x + 6 = be the value of a larger number
From the statement "The sum of two numbers is twice their difference.", then the working equation is
From the working equation, we can solve for the value of x which is the value of a smaller number as follows
The value of a larger number is
Therefore, the numbers are 6 and 18.
Category: Algebra
"Published in Vacaville, California, USA"
A customer in a coffee shop wishes to purchase a blend of two coffees: Kenyan, costing $ 3.50 a pound, and Sri Lankan, costing $ 5.60 a pound. He ends up buying 3 lbs of such as blend, which costs him $11.55. How many pounds of each kind went into the mixture?
Solution:
From the description of a given word problem, it is an application of linear equation with two equations, two unknowns.
Let x be the number of pounds of Kenyan coffee
y be the number of pounds of Sri Lankan coffee
From the statement "He ends up buying 3 lbs of such as blend,..", then the working equation is
From the statement "A
customer in a coffee shop wishes to purchase a blend of two coffees:
Kenyan, costing $ 3.50 a pound, and Sri Lankan, costing $ 5.60 a pound....which costs him $11.55.", then the working equation is
Hence, the working equations for the given problem are
From the first equation,
Substitute the value of x to the second equation, we have
Substitute the value of y to any of two equations, we have
Therefore, a customer needs to buy a mixture of 2.5 pounds of Kenyan coffee and 0.5 pounds of Sri Lankan coffee that cost $11.55.
Category: Algebra
"Published in Vacaville, California, USA"
A man has 14 coins in his pocket, all of which are dimes and quarters. If the total value of his change is $ 2.75, how many dimes and how many quarters does he have?
Solution:
From the description of a given word problem, it is an application of linear equation with two equations, two unknowns.
Let x = be the number of dimes or 10 cent coins
y = be the number of quarters or 25 cent coins
From the statement "A man has 14 coins in his pocket, all of which are dimes and quarters.", then the working equation is
From the statement "If the total value of his change is $ 2.75,..", then the working equation is
Hence, the working equations for the given problem are
From the first equation,
Substitute the value of y to the second equation, we have
Substitute the value of x to any of two equations, we have
Therefore, there are 5 coins of dime and 9 coins of quarter in his pocket.
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