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2 years ago

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Pedro sliced 27 cakes. Each chocolate cake had 7 slices and each lemon cake had 6 slices. If Pedro made 170 slices in total, how

many of each type of cake did he slice?

1 answer:

r-ruslan [8.4K]2 years ago

7 0

Answer:

Step-by-step explanation:

Let number of chocolate cakes = c

Number of lemon cakes = l

Total cakes = 27

c + l = 27 ---------------(I)

Total slices = 170

7c + 6l = 170 ---------------(II)

Multiply equation (i) by (-7) and then add. So, c will be eliminated and we can find the value of l

(I) * (-7) -7c - 7l = -189

(II) <u>7c + 6l = 170 </u> {Now add}

- l = -19

l = 19

Plugin l = 19 in equation (I)

c + 19 = 27

c = 27 - 19

c = 8

Number of chocolate cakes = 8

Number of lemon cakes = 19

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Calculate the arithmetic sequence in which a9=17 and the common difference is d=-2.1

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Answer:

$S_{31}=71.3$

Step-by-step explanation:

The nth term of an arithmetic sequence is given by the formula,

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We were given that the 9th term is $17$ .

$\Rightarrow 17=a_1+(9-1)(-2.1)$

$\Rightarrow 17=a_1+(8)\times(-2.1)$

$\Rightarrow 17=a_1-\frac{84}{5}$

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The sum of the first n-terms is given by the formula,

$S_n=\frac{n}{2}(2a_1+(n-1)d)$

To find $S_{31}$ , we substitute $n=31$ , $a_1=\frac{169}{5}$ and $d=-2.1$ .

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$\Rightarrow S_{31}=\frac{31}{2}(2(\frac{169}{5}+(30)(-2.1))$

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-6h plus 4 - 3plus h equals 11

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$- 6h + h = - 5h$
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Now we have;
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We then subtract 1 from both sides;
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Then we divide both sides by 5;
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$- 5h \div - 5h = h$
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Jake bought 2 shirts and 1 pair of pants for $6. Mike bought 1 shirt and 1 pair of pants for $4. How much is each shirt and each

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The cost of a shirt and a pair of pants is the same and is equal to $2. The correct option is B.

<h3>What is a solution to a system of equations?</h3>

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Let x represent the cost of a shirt, while y represent the cost of a pair of pants.

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Also, Mike bought 1 shirt and 1 pair of pants for $4. Therefore, the equation that represents this situation is,

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Solve the equation for x,

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Substitute the value of x in equation 1,

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Hence, the cost of a shirt and a pair of pants is the same and is equal to $2.

Learn more about finding the solution graphically here:

brainly.com/question/26254258

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