I Need Help with some word problems?

Question

This is Algebra 2 word problems and i need help because i try so many times and i still get the wrong answer.

1.A music dealer ran a sale of records and tapes.ecord were reduced to $7 each and tapes to $7.50 each.The dealer sold 60 more records than tapes for a total sale of $2160. How many records did the dealer sell?

2.The Senior Class officers sold slices of pizza for .75 each and hamburgers for $1.35 each.They sold 40 more slices of pizza than hamburgers, and sales totaled $292.50.How many slices of pizza did they sell?

3.The perimeter of a certain basketball court is 266 ft,and its length is 35 ft more than its width.Find the dimensions of the court.

4.If one side of a square is increased by 8cm and an adjacent side decreased by 2cm,a rectangle is formedwhose perimeter is 40cm. Find the length of a side of the square.

5.Jim's weekly pay is two thirds of Alicia's.Together they can earn $600 per week. What is each person's weekly pay?

Answer 1

1) Let t = the number of tapes sold, so t+60 would be the number of records sold. The price of tapes sold would be 7.5t, and the price of records sold would be 7(t+60). The equation for the total sale would then be 7.5t + 7(t+60) = 2160. Simplify the left side to read 14.5t + 420 = 2160. Subtract 420 from both sides to give 14.5t = 1740. Divide both sides by 14.5 to give t = 120. The dealer sold 120 tapes and 180 records. To check, multiply 120x7.5 and 180x7 and add the results.

2) Start with h = number of hamburgers and h+40 = number of pizzas. To avoid the decimals, use cents. The value of the burgers sold would be 135h, and the value of the pizzas sold would be 75(h+40). This is the same kind of problem as #1, so you should be able to take it from here.

3) Start with w = width, and w+35 = length. Put that into the formula for the perimeter of a rectangle: P = 2(l+w), and get 266 = 2(w+35+w). Simplify to 266 = 2(2w+35) = 4w + 70. Subtract 70 from both sides to give 196 = 4w. Divide both sides by 4 to get the width, then add 35 to that answer to get the length. Check by adding twice the width to twice the length.

4) Let s = length of the square's side. The rectangle's length will be s+8, and the width will be s-2. Put these and the 40 into the perimeter formula used in #3, and solve for s.

Answer 2

1. x = # tapes
x+60 = # records
7.5x +7(x+60) = 2160
7.5x +7x +420 = 2160
14.5x = 1740
x = 120 = # tapes sold
x+60 = 180 = # records sold

2. Same logic as in 1.

3. w = width
l= w+35
P = 2w + 2(w+35) = 266
4w +70 = 266
4w = 196
w = 49 feet
l = 49 +35 = 84 feet

s = side of square
s+8 = length of rectangle
s-2 = width of rectangle
2(s+8) +2(s-2) = 40
2s+16 +2s-4 = 40
4s = 28
s = 7 cm = side of square

Answer 3

1) 180 records sold
2) 165 slices of pizza sold
3) the court is 49 x 84
4) a side of the square is 7cm

Answer 4

1.
Let x be the number of records.
Balance by the total sale,
7x + 7.5(x-60) = 2160
Solve for x,
x = 180

All the four problems are very similar to each other. Could you follow the first one I solved to finish the remaining three?

Answer 5

What shapes do you get when you split the square with a diagonal? Two trangles. Since we know the field is a square, that means all the sides are equal (therefore, if you know one side, you know all the sides). So now you have a trangle with two sides equal to 60 feet. You can now use Pythagorean's theorem: A (squared) + B(squared) = C (squared) A and B are your two sides and then you just solve for C. Good luck!

Answer 6

180 records.
165 Pizzas....