Need help with these word problems!

[Guest]

If anyone could help me with these two word problems it would be greatly appreciated!

1. Kathi and Robert Hawn had a pottery stand at the annual Skippack Craft Fair. They sold some of their pottery at the original price of \$13.50 ​each, but later decreased the price of each by ​$2.002.00. If they sold all 9999 pieces and took in \$1,196.50​, find how many they sold at the original price and how many they sold at the reduced price.

2. Jen Butler has been pricing​ Speed-Pass train fares for a group trip to New York. Three adults and four children must pay \$92.  Two adults and three children must pay \$65.  Find the price of the​ adult's ticket and the price of a​ child's ticket.

[Guest]

2 task is very easy.
Decided the system:

[tex]\begin{array}{|l}3 x +4 y = 92 \\ 2x + 3y = 65 \end{array}[/tex]

I got it answered 16 $ , 11 $.

[Guest]

Jen butler has been pricing Speed-pass train fares for a group trip to New York. Three adults and four children must pay \$110. Two adults and three children must pay \$78. Find the price of the adult’s ticket and the price of a child’s ticket.

[Guest]

This is impossible! If they had sold all 9999 pieces at the lower price of \$13.50- 2.00= \$11.50, they would have brought in 9999(11.50)= \$114988.5, already much more than the \$1,196.50! You may have copied a number incorrectly. Possibly it was 999 pieces rather than 9999?

[Guest]

Jen butler has been pricing Speed-pass train fares for a group trip to New York.
Three adults and four children must pay \$110. Two adults and three children must pay \$78. Find the price of the adult’s ticket and the price of a child’s ticket.

Let A be the cost of an adult ticket and C be the cost of a child's ticket.

"Three adults and four children must pay $110."
So 3A+ 4C= 110.
"Two adults and three children must pay $78."
So 2A+ 3C= 78.

Can you solve 3A+ 4C= 110 and 2A+ 3C= 78 for A and C?

[HallsofIvy]

Since this one hasn't been addressed yet
"1. Kathi and Robert Hawn had a pottery stand at the annual Skippack Craft Fair. They sold some of their pottery at the original price of 13.50 ​each, but later decreased the price of each by ​2.00. If they sold all 9999 pieces and took in 1,196.50​, find how many they sold at the original price and how many they sold at the reduced price."

(I have dropped the dollar signs since they affect formatting.)

As usual start by "labeling" what we want to find: Let "x" be the number of pieces of pottery they sold at the original price, 13.50, and let "y" be the number of pieces of pottery they sold at the reduce price, 13.50- 2.00= 11.50. Since they sold 9999 pieces, x+ y= 9999. They got 13.50x dollars from the sale of the x pieces sold at the higher price and 11.50y dollars from the sale of the y pieces sold at the lower price. That means the got a total of 13.50x+ 11.50y= 1196.50.

We need to solve the two equations x+ y= 9999 and 13.5x+ 11.5y= 1196.5. From x+ y= 9999 we get y= 9999- x. Replacing y in the second equation by that, 13.5x+ 11.5(9999- x)= 13.5x- 114988.5+ 11.5x= 25x- 114988.5= 1196.5. Add 114988.5 to both sides to get 15.5x= 116185. Finally, divide both side by 15.5. That will give x, the number of pieces sold at 13.50 each. Since x+ y= 9999, y, the number of pieces they sold a 2.00 each, will be 9999- x.