Mathematics, 17.07.2019 17:00 860jay

Students in a cooking class made 4 1/2 quarts of soup. they served 4/5 of the soup to friends. each serving is 3/5 quart. hector incorrectly says that there were 3 3/5 serving of soup. what is the correct number of servings ? what did hector do wrong ?

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Answer from: 10040816

The correct number of servings of soup is 6.

What Hector did wrong was that he assumed that the total quarts that was served is the number of servings.

The first step to determine the answer is to determine the total quarts of soup that was served.

Quarts served = fraction served x quarts the class made

$\frac{4}{5}$ × $4\frac{1}{2}$

$\frac{4}{5}$ × $\frac{9}{2}$ = $\frac{18}{5}$ = $3\frac{3}{5}$

The second step is to determine the number of servings. In order to determine the number of servings, divide the quart of each serving by the total quarts served.

$\frac{18}{5}$ ÷ $\frac{3}{5}$

$\frac{18}{5}$ × $\frac{5}{3}$ = 6 servings

A similar question was answered here: link

Answer from: parrazm2022

So the students mad 4 and 1/2 quarts of soup.

they served 4/5 of that 4 and 1/2 to some friends....well, what's 4/5 of 4 and 1/2? well is just their product.

$\bf 4\frac{1}{2}\implies \cfrac{4\cdot 2+1}{2}\implies \cfrac{9}{2}\qquad\qquad \qquad \qquad \cfrac{9}{2}\cdot \cfrac{4}{5}\implies \cfrac{18}{5}$

so, each friend got to drink 3/5 quart, how many servings, and therefore friends, can one get out of 18/5 quarts of soup?

well, how many times does 3/5 go into 18/5? let's check.

$\bf \cfrac{\quad \frac{18}{5}\quad }{\frac{3}{5}}\implies \cfrac{18}{\underline{5}}\cdot \cfrac{\underline{5}}{3}\implies \cfrac{18}{3}\implies \stackrel{servings}{6}$

so, there were 6 servings, meaning there were 6 friends about.

now, whatever happened to Hector? well, 18/5 in mixed is 3 and 3/5, so he's correct, there were 3 and 3/5 "quarts in total" served to the friends, but each serving wasn't that much, was just a fraction of that.

Answer from: Quest

answer:

c 60% on edg

Answer from: Quest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is

$y\leq -x+4$

similarly, check the second related equation.

$3(1)=0$

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

$3y> x$

15 points write a system of inequalities to represent the shaded portion of the graph

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