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creativ13 [48]
3 years ago
11

Pensils are sold in packages of 10 and erasers are sold in packages of 6. What is the least number of pensils and erasers you ca

n buy so that there is one pencil for each eraser with none left over.
Mathematics
1 answer:
asambeis [7]3 years ago
8 0
To understand the problem consider the following cases.

i)

If we buy 1 packet of pencils, and 2 packet of erasers, 

we have 1*10=10 pencils and 2*6=12 erasers.

ii)

If we buy 3 packet of pencils, and 4 packet of erasers, 

we have 3*10=30 pencils and 4*6=24 erasers.


So let a and b be the correct number of packets of pencils and erasers respectively.

That is the least numbers a and b, such that 10a=6b.

10a=6b

divide both sides by 10:

a= \frac{6b}{10}= \frac{3b}{5}

divide both sides by b:

\frac{a}{b} =  \frac{3}{5}

the ratio a:b cannot be simplified any further. This means that the smallest (natural) numbers a and b such that \frac{a}{b} = \frac{3}{5} are a=3 and b=5


Answer:


3 packages of pencils, 5 packages of erasers.

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Identify the constant of proportionality for each direct variation below.
andriy [413]

Answer:

see explanation

Step-by-step explanation:

The equation of 2 quantities in direct proportion is

y = kx ← k is the constant of proportionality

1

y = - 4x ← in standard form

with k = - 4

2

\frac{y}{x} = 2 ( multiply both sides by x )

y = 2x ← in standard form

with k = 2

3

\frac{x}{y} = 3 ( multiply both sides by y )

x = 3y ( divide both sides by 3 )

\frac{1}{3} x = y ← in standard form

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What is the solution to<br><br>- 4x + 28 &gt; 12
raketka [301]

Answer:

\large\boxed{x

Step-by-step explanation:

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6 0
3 years ago
Could somebody check my work and tell me if it's right? If its wrong, please tell me where I went wrong.
vodka [1.7K]

Answer:

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4 0
3 years ago
Calculate the frequency in hertz of photons of light with energy of 8.10 × 10-19 J.
stira [4]
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We can solve the equation in terms of frequency to get
v= \dfrac{E}{h}

We substitute our given energy, 8.10 \times 10^{-19} J, and Planck's constant, 6.626 \times 10^{-34} Js.

v= \dfrac{8.10 \times 10^{-19} J}{6.626 \times 10^{-34} Js}=1.22 \times 10^{15} s^{-1}=1.22 \times 10^{15} Hz
5 0
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Marcy can make 3 potholders and 8 paper flowers in a day. The following expression, (3 * 2.50 + 8 * 1.25)d represents how much M
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Answer:

(3 * 2.50 + 8 * 1.25) d =

3*2.50 d + 8*1.25 d  

or  

7.50 d + 10 d

8 0
3 years ago
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