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lutik1710 [3]
3 years ago
14

A 40-inch board is to be cut into three pieces so that the second piece is 3 times as long as the first piece and the third piec

e 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.
What is the length of the first piece?
What is the length of the second piece?
What is the length of the third piece?
Mathematics
1 answer:
tiny-mole [99]3 years ago
8 0

Answer:

The first piece is 5 inches long, while the second is 15 inches and the third one is 20 inches.

Step-by-step explanation:

To determine the length of the 3 pieces, knowing that the total of the board is 40 inches, and that the second measures 3 times more than the first and the third measures 4 times more than the first, the following equation must be performed:

X + 3X + 4X = 40

8X = 40

X = 40/8

X = 5

Therefore, the first piece is 5 inches long, while the second is 15 inches and the third 20 inches.

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Combine like terms

-x = 4 + 6 - 3x
-x = 10 - 3x

Isolate the x, add 3x to both sides

-x (+3x) = 10 - 3x (+3x)

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Simplify. Combine like terms

-x + 3x = 10

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Isolate the x, divide 2 from both sides

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x = 10/2

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3. Sophie and Jackie each have a collection of baseball cards, Jackie has 5 more cards than
IRISSAK [1]

Answer:

Sophie has 12.5 cards

Step-by-step explanation:

Let

x -----> number of cards Sophie has

y -----> number of cards Jackie has

we know that

x+y=30 -----> equation A  

y=x+5 -----> equation B

Solve by substitution

Substitute equation B in equation A and solve for x

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Answer:

12

Step-by-step explanation:

We can see that the base TA is 4, and the second base RS is 2. We can see that the height is 4. The area of a trapezoid is:

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Using this, we can substitute, and get:

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Hope it helps!!

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