Question

Stella needs 555 grams of wool to knit a sweater, a hat, and a scarf. The hat requires one-fifth as much wool as the sweater and 5 grams more than the scarf. How many grams of wool does each item require?

Answer 1

The sweater requires 400 grams of wool, the hat requires 80 grams of wool, and the scarf requires 75 grams of wool.

Step-by-step explanation:

Let's assign variables to represent the amounts of wool needed for each item. Let's call the amount of wool needed for the sweater S, the amount for the hat H, and the amount for the scarf C.

We're given that the hat requires one-fifth as much wool as the sweater. So we can write the equation H = (1/5)S.

We're also given that the hat requires 5 grams more than the scarf. So we can write the equation H = C + 5.

Finally, we're told that Stella needs a total of 555 grams of wool. So we can write the equation S + H + C = 555.

We can solve this system of equations to find the values for S, H, and C.

From the equation H = (1/5)S, we can solve for S in terms of H: S = 5H.

Substituting this into the equation S + H + C = 555:

5H + H + C = 555

Combining like terms:

6H + C = 555

And substituting the equation H = C + 5:

6(C + 5) + C = 555

Simplifying and solving for C:

6C + 30 + C = 555

7C + 30 = 555

7C = 525

C = 75

Substituting this back into the equation H = C + 5:

H = 75 + 5 = 80

Finally, substituting this back into the equation S = 5H:

S = 5(80) = 400

Therefore, the sweater requires 400 grams of wool, the hat requires 80 grams of wool, and the scarf requires 75 grams of wool.