Question

Mrs. Hallmark wants to sell a box of two varieties of birthday cards for $5.80. The number of 30 cent cards is six more than one half the number of 35 cent cards. How many 35 cent cards are in the box?

a. 6
b. 8
c. 10
d. 12
e. None of these

Answer 1

By setting up a system of equations and substituting, we find that there are 8 cards that cost 35 cents each. Option b is the correct answer.

Step-by-step explanation:

The question asks to determine the number of 35 cent cards in a box, given the total price and a relationship between the number of 30 cent and 35 cent cards. To solve this, we can set up a system of equations. Let's denote the number of 35 cent cards as x and the number of 30 cent cards as y. According to the problem, we have the following equations:

• The total cost of the cards is $5.80: 0.35x + 0.30y = 5.80
• The number of 30 cent cards is six more than one half the number of 35 cent cards: y = 0.5x + 6

Insert the second equation into the first to find the value of x.

0.35x + 0.30(0.5x + 6) = 5.80
0.35x + 0.15x + 1.8 = 5.80
0.50x = 4
x = 8

So, there are 8 cards that cost 35 cents each in the box, which corresponds to option b.