1.
a) On Wednesday, Harry sold 3 times as many candy bars as on Tuesday. On Thursday, he sold 5 times as many bars as on Wednesday. He sold a total of 152 candy bars. How many did he sell each day?
b) Bill has 5 times as many baseball cards as Fred. Tim has 3 fewer than 4 times as many baseball cards as Fred. In all they have 167 baseball cards. How many does each have?
2.
a) The length of a rectangle is 5 more than the width. The perimeter of the rectangle is 168 inches. Find the dimensions of the rectangle.
b) The length of a rectangle is twice the width. If the length is increased by 4 inches and the width is diminished by 1 inch, a new rectangle is formed whose perimeter is 198 inches. Fine the dimensions of the original rectangle.
I really don"t understand word problems can someone help me on how to make equations on these
In most of these you simply have to translate from English to Math.
I will do #2 b)
original rectangle:
"The length of a rectangle is twice the width"
since "width" is the reference , let the width be x inches
then the length must be 2x inches
new rectangle:
"the length is increased by 4" ---> length = 2x+4
"the width is diminished by 1" ----> width = x - 1
perimeter of new rectangle is 198 ----> twice the length + twice the width = 198
2(2x+4) + 2(x-1) = 198
4x + 8 + 2x - 2 = 198
6x = 192
x = 32
original width = 32 inches
original length = 64 inches
new width = 31
new length = 68
new perimeter = 2(31) + 2(68) = 198
My answer is correct
Follow my method, perhaps highlighting or underlining the important phrases to form your variables.
Certainly! Word problems can sometimes be challenging, but breaking them down and creating equations can help simplify the problem-solving process. Let's go through each problem step by step:
1. a) To solve this problem, let's define some variables:
- Let "x" represent the number of candy bars sold on Tuesday.
- Since Harry sold three times as many candy bars on Wednesday, the number of candy bars sold on Wednesday would be 3x.
- Similarly, the number of candy bars sold on Thursday would be 5 times the number sold on Wednesday, which is 5(3x) = 15x.
Now, the total number of candy bars sold is given as 152, so we can create an equation:
x + 3x + 15x = 152
Simplifying this equation, we get:
19x = 152
x = 152 / 19
x = 8
Therefore, Harry sold 8 candy bars on Tuesday, 3 * 8 = 24 candy bars on Wednesday, and 15 * 8 = 120 candy bars on Thursday.
1. b) Let's define variables for this problem too:
- Let "x" represent the number of baseball cards that Fred has.
- Bill has 5 times as many cards as Fred, so Bill has 5x cards.
- Tim has 3 fewer than 4 times the number of cards Fred has, so Tim has (4x - 3) cards.
The total number of baseball cards is given as 167, so we can create an equation:
x + 5x + (4x - 3) = 167
Simplifying this equation, we get:
10x - 3 = 167
10x = 167 + 3
10x = 170
x = 170 / 10
x = 17
Therefore, Fred has 17 baseball cards, Bill has 5 * 17 = 85 baseball cards, and Tim has 4 * 17 - 3 = 68 baseball cards.
2. a) To solve this problem, let's again define some variables:
- Let "x" represent the width of the rectangle.
- Since the length is 5 more than the width, the length would be (x + 5).
The perimeter of a rectangle is found by adding the lengths of all sides. In this case, the perimeter is given as 168, so we can create an equation:
2(x + 5) + 2x = 168
Simplifying this equation, we get:
2x + 10 + 2x = 168
4x + 10 = 168
4x = 168 - 10
4x = 158
x = 158 / 4
x = 39.5
Since dimensions cannot be in decimal form, we round it to the nearest whole number. Therefore, the width is 40 inches and the length is x + 5 = 40 + 5 = 45 inches.
Hence, the dimensions of the rectangle are 40 inches (width) and 45 inches (length).
2. b) Let's define variables for this problem:
- Let "x" represent the width of the original rectangle.
- Since the length is twice the width, the length would be 2x.
In the new rectangle, the length is increased by 4 inches (2x + 4) and the width is diminished by 1 inch (x - 1). The perimeter is given as 198, so we can create an equation:
2(2x + 4) + 2(x - 1) = 198
Simplifying this equation, we get:
4x + 8 + 2x - 2 = 198
6x + 6 = 198
6x = 198 - 6
6x = 192
x = 192 / 6
x = 32
Therefore, the width of the original rectangle is 32 inches, and the length is 2x = 2 * 32 = 64 inches.
Hence, the dimensions of the original rectangle are 32 inches (width) and 64 inches (length).
I hope this explanation helps you understand how to set up equations for word problems and solve them. If you have any further questions, feel free to ask!