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Nutka1998 [239]
1 year ago
13

Samuel and Jason spent 3/4 of their combined earnings from 100 by gift. How much do they spend? Is there enough left over from W

ednesday’s earnings to buy a card that cost $3.25
Mathematics
1 answer:
-Dominant- [34]1 year ago
7 0

They spend $5.88 on a gift, but there is not enough money left over to spend $3.25 on a card, if Samuel and Jason spent 3/4 of their combined earnings from 100 by gift.

<h3>Define equation.</h3>

A formula that expresses the connection between two expressions on each side of a sign is called equation. Typically, it has a single variable and an equal sign. Like this: 2x - 4 Equals 2.

Given,

Samuel and Jason spent 3/4 of their combined earnings from 100 by gift.

Samuel and Jason's profits as of Wednesday are as follows:

Earnings for Samuel:

12.5 x 40  

$5.

Earnings for Jason are

7.1 x $0.40

$2.84.

The total revenue for Wednesday is:

Samuel's and Jason's combined incomes are equal.

Earnings totaled

$5 + $2.84 = $7.84

The money that was spent is:

Total income multiplied by 34 equals spent income.

Earnings spent = 7.84 x 1/4

Earnings spent =  $5.88

The remainder is:

Equation

Leftover = Total Earnings - Spent Earnings

7.84 - 5.88 =  $1.96 in leftovers.

They spend $5.88 on a gift, but there is not enough money left over to spend $3.25 on a card.

To learn more about equation, visit:

brainly.com/question/2420339

#SPJ1

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\bf ~~~~~~~~\textit{binomial theorem expansion} \\\\ \qquad \qquad (1+ax)^n\implies \begin{array}{llll} term&coefficient&value\\ \cline{1-3}&\\ 1&+1&(1)^n(ax)^0\\\\ 2&+\frac{(1)(n)}{1}\to n&(1)^{n-1}(ax)^1\\\\ 3&+\frac{n\cdot (n-1)}{2}&(1)^{n-2}(ax)^2 \end{array}

so, following that to get the next coefficient, we get those equivalents as you see there for the 2nd and 3rd terms.

so then, we know that the expanded 2nd term is 24x therefore

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\bf \cfrac{n(n-1)}{2}~~(1)^{n-2}(ax)^2 = 240x^2\implies \cfrac{n(n-1)}{2}(1)(a^2x^2) = 240x^2 \\\\\\ \cfrac{(n^2-n)(a^2x^2)}{2}=240x^2\implies \cfrac{(n^2-n)(a^2)}{2}=\cfrac{240x^2}{x^2}\implies \cfrac{a^2n^2-a^2n}{2}=240 \\\\\\ a^2n^2-a^2n=480

but but but, we know what "n" equals to, recall above, so let's do some quick substitution

\bf a^2n^2-a^2n=480\qquad \boxed{n=\cfrac{24}{a}}\qquad a^2\left( \cfrac{24}{a} \right)^2-a^2\left( \cfrac{24}{a} \right)=480 \\\\\\ a^2\cdot \cfrac{24^2}{a^2}-24a=480\implies 24^2-24a=480\implies 576-24a=480 \\\\\\ -24a=-96\implies a=\cfrac{-96}{-24}\implies \blacktriangleright a = 4\blacktriangleleft \\\\[-0.35em] ~\dotfill\\\\ n=\cfrac{24}{a}\implies n=\cfrac{24}{4}\implies \blacktriangleright n=6 \blacktriangleleft

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<h2>stay safe healthy and happy.....</h2>
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