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3 years ago

A machine produces 75 widgets an hour. How many widgets does it produce in 6 minutes

Mathematics

2 answers:

Pachacha [2.7K]3 years ago

8 0

we know that

A machine produces $75$ widgets an hour

How many widgets does it produce in $6$ minutes?

one hour is equal to ------> $60\ minutes$

by proportion

$\frac{75}{60} =\frac{x}{6} \\\\ 60*x= 75*6\\\\ x=\frac{75*6}{60}$

$x=7.5\ widgets$

therefore

<u>the answer is</u>

A machine produces $7\ widgets$ in $6$ minutes

inn [45]3 years ago

5 0

75/60 is 1.25 and 1.25 times 6 is 7.5 but you can't produce a half widget so it is just 7

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Solve the system of equations by substitution. 3/8 x + 1/3 y =17/24 and <br> x + 7y = 8

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$\left \{ {{ \frac{3}{8}x+ \frac{1}{3}y = \frac{17}{14} } \atop {x+7y=8}} \right.$

To solve this system by substitution, first isolate x in the second equation.

$x+7y=8$
$x+7y-7y=8-7y$
$x=8-7y$

Now, plug this expression ( $8-7y$ ) for x in the top equation to solve for y.

$\frac{3}{8} (8-7y)+ \frac{1}{3} y= \frac{17}{14}$
$3- \frac{21}{8} y+ \frac{1}{3} y= \frac{17}{24}$
$72-63y+8y=17$
$72-55y=17$
$-55y=17-72$
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$y=1$

Now that you have y, plug it into the second equation and solve for x.

$x+7y=8$
$x+7(1)=8$
$x+7=8$
$x=1$

Last step is to plug your x- and y-values in to both equations to check your work.

$\frac{3}{8} (1)+ \frac{1}{3} y= \frac{17}{24}$

$\frac{3}{8} * \frac{3}{3} = \frac{9}{24} ; \frac{1}{3} * \frac{8}{8} = \frac{8}{24}$

$\frac{9}{24} + \frac{8}{24} = \frac{17}{24}$ <--True

$1+7(1)=8$
$1+7=8$ <--True

Answer:
$x=1 \\ y=1$

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