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adoni [48]
3 years ago
13

Peter is trying to buy fencing for the perimeter of his garden. His garden is in the shape of a rectangle with a length of 2(x+6

)feet and a width of 3.5x feet. How many feet of fencing will he need to buy? Write and simplify an expression to represent this situation? What properties did you use?
SHOW ALL WORK
Mathematics
1 answer:
RideAnS [48]3 years ago
4 0

Given dimensions of a rectangular garden are:

length = 2(x+6) feet

width = 3.5x feet

using the distributive property on length we get, length = 2x+12

Perimeter of a rectangle is 2(length+width)

So, P = 2(2x+12+3.5x)

Solving it we get,

P = 2(5.5x +12)   ..............adding like terms

P = (2\times5.5)+(2\times12) .............multiplying and adding

P = 11x+24

So, perimeter is 11x+24 feet. This value of fencing will be needed.

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Carrie has 40 more nickels than Joan has dimes. They both have the same amount of money. How many coins does each girl have? Wha
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Answer:

Carrie and Joan have 80 nickels and 40 dimes, respectively, and each one has an amount of money of 4 US dollars.

Step-by-step explanation:

Let be x and y the amounts of nickels and dimes that Carrie and Joan have, as c the total amount of money that both Carrie and Joan have. A nickel is a five cent coin and a dime is a ten cent coin.

The following equations are constructed after a careful reading on statement:

Carrie's amount of money:

0.05\cdot x = c (Eq. 1)

Joan's amount of money:

0.10\cdot y = c (Eq. 2)

Relation between amounts of coins:

x = y+40 (Eq. 3)

First we eliminate c by equalizing (Eq. 1) and (Eq. 2):

0.05\cdot x = 0.10\cdot y

Then, we reduce the resulting formula by (Eq. 3):

0.05\cdot (y+40) = 0.10\cdot y

y+40 = 2\cdot y

y = 40

And rest of variable are now determined:

x = 40+40

x = 80

c = 0.05\cdot (80)

c  = 4

Carrie and Joan have 80 nickels and 40 dimes, respectively, and each one has an amount of money of 4 US dollars.

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