At Gwen's garage sale, all books were one price, and all magazines were another price. Harriet bought four books and three magazines for 1.45, and June bought two books and five magazines for 1.25. What was the price of a book and what was the price of a magazine?
Let x be the book price and y be the magazine price, both in cents. Your statements about the two purchases can be written
4x + 3y = 145
and
2x + 5y = 125
Now solve those two equations for x and y. A good first step would be to convert (double both sides of) the second equation to give you
4x + 10 y = 250
Combining that with the first equation can eliminate the x variable and give you
7 y = 105
y = 15 cents
We will be happy to critique your work
To solve this problem, we can set up two equations based on the given information.
Let's represent the price of a book as x (in cents) and the price of a magazine as y (in cents).
From the information given, we know that Harriet bought four books and three magazines for 1.45 (or 145 cents). This can be written as:
4x + 3y = 145
Similarly, June bought two books and five magazines for 1.25 (or 125 cents). This can be written as:
2x + 5y = 125
To solve these equations, we can use the method of substitution or elimination.
Let's use the elimination method in this case. Multiply the second equation by 2 to get:
4x + 10y = 250
Now we have two equations:
4x + 3y = 145
4x + 10y = 250
Subtracting the first equation from the second equation will eliminate the x variable:
(4x + 10y) - (4x + 3y) = 250 - 145
7y = 105
Now divide both sides of the equation by 7:
y = 105 / 7
y = 15
Therefore, the price of a magazine is 15 cents.
To find the price of a book, we can substitute the value of y (15) into any of the original equations. Let's use the first equation:
4x + 3(15) = 145
4x + 45 = 145
4x = 145 - 45
4x = 100
x = 100 / 4
x = 25
So, the price of a book is 25 cents.
Therefore, the price of a book is 25 cents and the price of a magazine is 15 cents.