Mathematics, 29.09.2019 15:10 cotybuge2701

Mr. rodriguez is packing bags of snacks for his children’s lunchboxes. if he has 20 blueberries and 30 grapes, what is the maximum number of bags of snacks that he can pack so that each bag has the same number of blueberries and grapes?

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Answer from: kidlol

The maximum number of bags is 10 with 2 blueberries and 3 grapes every one.

Step-by-step explanation:

The maximum number of bags of snacks that he can pack so that each bag has the same number of blueberries and grapes is calculate finding the greatest common factor between 20 and 30.

First, it is necessary to identify all the factors of 20 and 30. Then, identify what are the factor that are equal in both cases and choose the greatest one. This is:

20 can be calculate as:

1 x 20 = 20

2 x 10 = 20

4 x 5 = 20

Then, the factors of 20 are: 1, 2, 4, 5, 10 and 20

At the same way, 30 can be calculate as:

1 x 30 = 30

2 x 15 = 30

3 x 10 = 30

5 x 6 = 30

Then, factors of 30 are: 1, 2, 3, 5, 6, 10, 15 and 30

Now, from these factors, the numbers 1, 2, 5 and 10 are factors of both numbers and the greatest one is 10. So, the greatest common factor of 20 and 30 is 10.

That means that the maximum number of bags of snacks that he can pack is 10. So, the number of blueberries that are going to be in every bag is calculate as:

$\frac{20 Blueberries}{10 Bags} = 2 Blueberries$

And, the number of grapes in every bag is:

$\frac{30 Grapes}{10 Bags} = 3 Grapes$

Answer from: Quest

for this case we must apply distributive property to the following expression:

$-2 (2.1x + 3y-0.8)$

the distributive property states that:

$(a + b) (c + d) = ac + ad + bc + bd$

then, when applying the property we have to multiply the -2 for each term within the parenthesis:

$-4.2x-6y + 1.6$

Answer from: Quest

First, think of what you know. you know that the number t the end of the equation will need to be subtracted because it is the money he lost from buying the lawn mower. and your first two weeks have negative profit, so that tells you that c and d are wrong. now you can plug any of the weeks into a and b to see which one works. i'll start with plugging week 1 into a. $y = 60(1) - 90 \\ y = 60 - 90 \\ y = - 30$ this isn't right because it says your answer for week one should be -90.so now we need to try the same thing with b. $y = 60(1) - 150 \\ y = 60 - 150 \\ y = - 90$ this one got you the right answer, (sometimes if you only check with one of the weeks multiple will work so you need to check with more of the weeks, but it worked out fine here)this means that b is the correct answer.let me know if you need more clarification. i hope this : )

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