Question

Mrs. Hallmark wants to sell a box of two varieties ofbirthday cards for $5.80. The number of 30¢ qards is sixmore than one half the number of 35€ cards. The numberof 35€ cards is:

Answer 1

Let's use the variable 'x' to represent the number of 30c cards and the variable 'y' to represent the number of 35c cards.

If the total price of the box is $5.80, we can write the equation:

`0.30x+0.35y=5.80`

If the number of 30c cards is six more than half the number of 35c cards, we have that:

`x=6+0.5y`

Using this value of x in the first equation, we have:

`\begin{gathered} 0.3(6+0.5y)+0.35y=5.8 \\ 1.8+0.15y+0.35y=5.8 \\ 0.5y=5.8-1.8 \\ 0.5y=4 \\ y=(4)/(0.5)=8 \end{gathered}`

So the number of 35 cards is 8.