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Yuki888 [10]
3 years ago
6

Sumeet is building two types of birdhouses. The more traditional type takes 4 pieces of wood and 2 hours to build. The more lavi

sh type takes 10 pieces of wood and 7 hours to build. If he has a total of 46 pieces of wood and 29 hours to work, then how many of each type of birdhouse can he build?

Mathematics
1 answer:
mina [271]3 years ago
8 0

Answer:

The no. of traditional type birdhouses are 4 and the no. of lavish type birdhouses are 3.

Step-by-step explanation:

Let x be the no. of traditional type birdhouses

The more traditional type takes 4 pieces of wood and 2 hours to build.

One house requires wood = 4

x houses requires wood = 4x

One house requires time = 2 hours

x houses requires time = 2x

Let y be the no. of lavish type birdhouses

The more lavish type takes 10 pieces of wood and 7 hours to build.

One house requires wood = 10

y houses requires wood = 10y

One house requires time = 7 hours

y houses requires time = 7y

Now we are given that he has a total of 46 pieces of wood and 29 hours to work,

So, equations becomes : 4x+10y = 46\\2x+7y=29

Plot these equations on graph

4x+10y = 46 ---Blue line

2x+7y=29  ---Green line

Refer the attached figure

The intersection point provides the solution

Intersection point : (4,3)

So, x = 4 and y = 3

Hence the no. of traditional type birdhouses are 4 and the no. of lavish type birdhouses are 3.

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2 years ago
23:
irina [24]

Answer:

(-\frac{3}{7}, 0) -- x intercept

(0,3) -- y intercept

Step-by-step explanation:

Given

y = 7x + 3

Required

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For x intercept.

Set y = 0

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y = 7x + 3

0 = 7x + 3

Collect Like Terms

7x = -3

Make x the subject

x = -\frac{3}{7}

Hence, the x intercept is: (-\frac{3}{7}, 0)

For the y intercept;

Set x = 0

So, we have:

y = 7x + 3

y = 7*0 + 3

y = 0 + 3

y = 3

Hence, the y intercept is: (0,3)

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