SOLUTION: mr rich had a custom built sandbox made forhis young son. In order to personalize it he required that the width be 7 feet less than 3 times his young sons age and the length be 4 f

Algebra ->  Human-and-algebraic-language -> SOLUTION: mr rich had a custom built sandbox made forhis young son. In order to personalize it he required that the width be 7 feet less than 3 times his young sons age and the length be 4 f      Log On


   

Question 591429: mr rich had a custom built sandbox made forhis young son. In order to personalize it he required that the width be 7 feet less than 3 times his young sons age and the length be 4 feet more than 2 his sons age. the Perimeter has to be his own age of 54 years old. Find the sons age and use it to find the dimensions of the sandbox
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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In order to personalize it he required that the width be 7 feet less than 3 times his young sons age and the length be 4 feet more than 2 his sons age.
the Perimeter has to be his own age of 54 years old.
Find the sons age and use it to find the dimensions of the sandbox
:
let s = the son's age
then
"the width be 7 feet less than 3 times his young sons age"
w = 3s-7
:
"the length be 4 feet more than 2 his sons age."
L = 2s+4
:
"Perimeter has to be his own age of 54 years old."
p = 54
2L + 2W = 54
Simplify, divide by 2
L + w = 27
L = (27-w)
:
Replace L with (2s+4), replace w with (3s-7)
2s + 4 = 27 - (3s-7)
2s + 4 = 27 - 3s + 7
Combine like terms
2s + 3s = 27 + 7 - 4
5s = 30
s = 6 yrs old is his son's age
:
Find w
w = 3(6)-7
w = 11 ft wide
find L
L = 2(6)+4
L = 16 ft long
:
:
Check this by finding the perimeter using these dimensions
2(16) + 2(11) =
32 + 22 = 54; confirm our solutions