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erastovalidia [21]
3 years ago
14

Stacey and Michele both babysit in the evening.staceys hours rate is $10 for one child plus $2per additional child Michael hourl

y rate $8 for one child plus $3per additional child.
The Thompson family pays the same hourly rate for Stacy or Michael.how many children are in the Thompson family
Mathematics
2 answers:
lara31 [8.8K]3 years ago
7 0
They have two children...
8 + 3c = 10 + 2c
c = 2
OleMash [197]3 years ago
7 0

Answer:  The number of children in the Thomson family is 3.

Step-by-step explanation:  Given that Stacey and Michele both babysit in the evening. Stacey's hours rate is $10 for one child plus $2 per additional child and Michael hourly rate $8 for one child plus $3 per additional child.

We are to find the number of children in the Thomson family if they pay the same hourly rate for Stacy and Michael.

Let the number of children in the Thomson family be denoted by n.

Then, according to the given information, we have

10+2\times(n-1)=8+3\times(n-1)\\\\\Rightarrow 10+2n-2=8+3n-3\\\\\Rightarrow 2n+8=3n+5\\\\\Rightarrow 3n-2n=8-5\\\\\Rightarrow n=3.

Therefore, there are three children in the Thomson family.

Thus, the number of children in the Thomson family is 3.

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Ms. Nina has 10 lbs of 25% sugar syrup. How much water does she need to add to make 10% sugar syrup?
ryzh [129]
She has 10lbs of 25% syrup... so, in the 10lbs, 25% of that is syrup, the rest, namely the 75% remaining is water or other substances.

let's say she adds "x" lbs of water, to get "y" lbs for the 10% mixture.

how much is 25% of 10lbs?  well, (25/100) * 10, or 2.5.

the water has no sugar syrup in it, so is just pure water, so the amoun of syrup in it is 0%, how much is 0% of "x" lbs?  well, (0/100) * x, or 0.00x, which is just 0.

how much is 10% of "y" lbs?  well (10/100) * y, or 0.10y.

whatever "x" and "y" are, we know that 10 + x = y.

we also know that the syrup amount in that is also 2.5 + 0.00x = 0.10y, thus


\bf \begin{array}{lccclll}
&\stackrel{lbs}{syrup}&\stackrel{concentration~\%}{syrup}&\stackrel{concentration}{amount}\\
&------&------&------\\
\textit{25\% syrup}&10&0.25&2.5\\
\textit{pur water}&x&0.00&0.00x\\
------&------&------&------\\
\textit{10\% mixture}&y&0.10&0.10y
\end{array}
\\\\\\
\begin{cases}
10+x=\boxed{y}\\
2.5+0.00x=0.10y\\
----------\\
2.5 = 0.10\left( \boxed{10+x} \right)
\end{cases}
\\\\\\
2.5=1 + 0.10x\implies 1.5=0.10x
\\\\\\
\cfrac{1.5}{0.10}=x\implies 15=x
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Step-by-step explanation:  We are given five different options and we are to select which explanation is correct to derive the formula for a circumference of a circle.

Let 'C' be the circumference and 'd' be the diameter of a circle. Now, we will write the ratio of the circumference to the diameter as

\dfrac{\textup{C}}{\textup{d}}.

Also, we know that

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And diameter of a circle is twice the radius, so

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Of the numbers 8, 9, 10, 11, and 12, which are solutions to the inequality 8p<84?
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<span>8p<84
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answer
</span><span>8, 9, 10 are solutions</span>
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