Download Unit 1 Assignment 9 Part 1 Section 2.5: Introduction to Problem

Unit 1 Assignment 9 Part 1
Section 2.5: Introduction to Problem-Solving
Write the following as an equation. Then solve.
1. The sum of six times a number, and 2, is equal to five times the number.
*SUM means ADD!
6x + 2 = 5x
NOW SOLVE!
2. If the sum of a number and 4 is tripled, the result is three less than twice the number.
TRIPLED means times 3 with parentheses! Don’t forget to switch the order when you see “LESS
THAN!”
3(x + 4) = 2x – 3
3. The sum of three consecutive integers is 183. What are the integers?
Remember, consecutive integers are one right after the other.
x = 1st integer
x + 1 = 2nd integer
x + 2 = 3rd integer
4. The left and right page numbers of an open book are two consecutive integers whose sum is 551.
Find the page numbers.
*This one works EXACTLY like the last one, except you only have 2 integers!
5. To make an international telephone call, you need the code for the country you are calling. The
codes for country A, country B, and C are three consecutive integers whose sum is 93. Find the
code for each country.
*JUST like #4!
6. A 21-inch board is to be cut into three pieces so that the second piece is twice as long as the first
piece and the third piece is 4 times as long as the first piece. If x represents the length of the first
piece, find the lengths of all three pieces.
x = length of the first piece
2x = length of the second piece
4x = length of the third piece
7. The sum of the speeds of two planes is 718.5 miles per hour. If the speed of the first plane is 7.5 mph
faster than the second plane, find the speeds of each plane.
Unit 1 Assignment 9 Part 2
Section 2.7:
Percent
1) What number is 13% of 90?
“What number”
is
x
=
13% “of” 90
multiply
.13 (9)
2) The number 21.5 is what percent of 86?
21.5
21.5
is
=
“what percent” “of” 86
x (86)
3) 32 is 10% of what number?
32
is
10% “of” “what number”
(change 10% to a decimal)
32 = (.10)x
Discount and Markup/Tip:
4)
For discounts, subtract! For markup or tip, add!
A used automobile dealership recently reduced the price of a compact car by 9%. If the price of
the car before discount was $18,800, find the discount and the new price.
Discount =(discount percent as a decimal)(original price)
Discount = (
)(
) = __________
Sale price = Original price – discount
Sale price = $18,800 - __________ = __________
5) A birthday meal is $42.60 including tax. Find the total cost if a 15% tip is added to the cost of the
meal.
Tip = (percent of tip as a decimal)(cost of meal)
Tip = (
)(
) = __________
Total cost = Meal cost + tip
Total cost = 42.60 + __________ = __________
6)
Find the original price of a pair of shoes if the sale price is $70 after a 30% discount.
7)
The number of farms in the country was 2.21 million in 2000. By 2006, the number had dropped
to 2.07 million. What was the percent of decrease? Round to the nearest tenth of a percent.
*Subtract, divide by the original amount, move the decimal!