I am having a hard time figuring out the equations for these problems.
1) The perimeter of a rectangle is 160 feet. One fourth the length is the same as twice the width. Find the demensions for the rectangle.
2) Lorena bought 10 packs of styrofoam cups for the graduation dance. A pack of fity 12-oz cups costs $1.80 and a pack of fifty 16-oz cups costs $2.40. Lorena paid a total of $21.60 excluding tax. How many packs of each size cup did shy buy?
3) The Taylor family reunion had a record turnout of 38 people last year. For a change of pace, they decided to go ice skating instead of having a picnic. Admission for the group cost was $153.50 [including skates]. How many adults and children were at the reunion?
Admission:
Adults-----$2.75
Children--$1.50
Admission and skate rental:
Adults-----$4.25
Children---$3.75
I really need help, please.
I will do one of them, then you try the others.
length = L
width = b
160 = 2L + 2 b
but
L/4 = 2 b
L = 8 b
so use 8 b for L
160 = 2 (8 b) + 2 b
160 = 18 b
b = 80/9
L = 8*80/9 = 640/9
check
160/9 + 1280/9 = 160, check
160/9 = 160/9 check
okay, is it okay if you can check my work later after I solve them ?
I'm here to help you understand how to solve these problems step by step. Let's start with the first problem:
1) The perimeter of a rectangle is 160 feet. One-fourth the length is the same as twice the width. Find the dimensions for the rectangle.
To solve this problem, we need to set up equations based on the given information.
Let's assume the length of the rectangle is L, and the width is W.
We know that the perimeter of a rectangle is given by the formula: P = 2L + 2W.
From the given information, we have two pieces of information:
- The perimeter of the rectangle is 160 feet: 2L + 2W = 160.
- One-fourth the length is the same as twice the width: (1/4)L = 2W.
Now, we can use these equations to solve for L and W.
First, let's rearrange the second equation to make L the subject:
L = 8W.
Now, substitute this value of L into the first equation:
2(8W) + 2W = 160.
Simplifying the equation:
16W + 2W = 160,
18W = 160,
W = 8.89.
Now, substitute the value of W back into the second equation to solve for L:
L = 8(8.89),
L = 71.10.
So, the dimensions of the rectangle are approximately 71.10 feet by 8.89 feet.
Let me know if you need any further clarification or have any other questions.