555 grams of wool were needed to knit a sweater, a hat, and a scarf. the hat required 5 times less wool than the sweater and 5 grams more than the scarf. how many grams of wool did each item require?
pls !

The grams of wool needed to knit a sweater was 400 grams

The grams of wool needed to knit a hat was 80 grams

The grams of wool needed to knit a scarf was 75 grams

Step-by-step explanation:

Let

x > grams of wool needed to knit a sweater

y > grams of wool needed to knit a hat

z > grams of wool needed to knit a scarf

we know that

x+y+z=555 > equation A

y=x/5 > x=5y > equation B

y=z+5 ---> z=y-5 > equation C

substitute equation B and equation C in equation A and solve for y

(5y)+y+(y-5)=555

7y=555+5

7y=560

y=80 grams

Find the value of x

x=5(80)=400 grams

Find the value of z

Z=80-5=75 grams

therefore

The grams of wool needed to knit a sweater was 400 grams

The grams of wool needed to knit a hat was 80 grams

The grams of wool needed to knit a scarf was 75 grams

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.

step-by-step explanation: it is d