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kolbaska11 [484]
3 years ago
10

Brian and Zack went to the store and bought packs of gum. Brian bought 3 less packs than twice the number zack bought. Together

they bought a total of 30 packs of gum. How many packs did each of them buy?
Mathematics
1 answer:
balu736 [363]3 years ago
3 0

Answer:

  • Zack: 11
  • Brian: 19

Step-by-step explanation:

Let z and b represent the number of packs that Zack and Brian bought, respectively. Then the problem statement tells us ...

  b = 2z -3 . . . . . . . Brian bought 3 fewer than twice what Zack bought

  b + z = 30 . . . . . . they bought a total of 30 packs

Using the first equation to substitute into the second, we have ...

  (2z -3) +z = 30

  3z -3 = 30

  3z = 33 . . . . . . add 3

  z = 11

  b = 2·11 -3 = 22 -3 = 19

_____

<em>Check</em>

  b + z = 19 + 11 = 30 . . . . answer checks OK

Zack bought 11 packs; Brian bought 19 packs of gum.

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2 years ago
Stefan sells Jim a bicycle for $175 and a helmet for $17. The total cost for Jim is 160% of what Stefan spent originally to buy
Nady [450]

Answer:

Stefan spend $120 originally.

Stefan made $72 by selling bicycle and helmet to Jim.

Step-by-step explanation:

Given:

Cost of bicycle = $175

Cost of Helmet = $17

Percent of total cost of Jim = 160% of original cost of Stefan

We need to find the Amount Stefan spend originally and money he made by selling the bicycle and helmet to Jim.

Solution:

Let the Amount Stefan spend originally be 'x'.

Total Cost of Jim is equal to sum of Cost of bicycle and Cost of Helmet.

framing in equation form we get;

Total Cost of Jim = 175+17 =\$192

Now we know that;

Total Cost of Jim is equal to 160% of  Amount Stefan spend originally.

framing in equation form we get;

192 = \frac{160}{100}\times x\\\\192 =1.6x

Dividing both side by 1.6 we get;

\frac{192}{1.6}=\frac{1.6x}{1.6}\\\\x= \$120

Hence Stefan spend $120 originally.

Now we can say that;

Money Stefan made is equal to Money Stefan spend originally minus Total Cost of Jim.

framing in equation form we get;

Money Stefan made = 192-120 =\$72

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7 0
3 years ago
Please help, I’m very confused
snow_tiger [21]

Answer:

1st picture: (0,4)

The lines intersect at point (0,4).

2nd picture: Graph D

2x ≥ y - 1

2x - 5y ≤ 10

Set these inequalities up in standard form.

y ≤ 2x + 1

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When you divide by a negative number, you switch the inequality sign.

Now you have:

y ≤ 2x + 1

y ≥ 2/5x - 2

Looking at the graphs, you first want to find the lines that intersect the y-axis at (0, 1) and (0, -2).

In this case, it is all of them.

Next, you would look at the shaded regions.

The first inequality says the values are less than or equal to. So you look for a shaded region below a line. The second inequality says the values are greater than or equal to. So you look for a shaded region above a line.

That would mean Graph B or D.

Then you look at the specific lines. You can see that the lower line is y ≥ 2/5x - 2. You need a shaded region above this line. You can see the above line is y ≤ 2x + 1. You need a shaded region below this line. That is Graph D.

8 0
3 years ago
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postnew [5]

Answer:

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