Let x = hat (because the hat is 5x LESS wool)
Let 5x = sweater (because it is 5x MORE wool than the hat)
Let x - 5 = scarf (because it is 5 g LESS than the amount for hat)
Now set up equation. Everything added must be equal to 555g which were used.
x + 5x + (x-5) = 555
6x + x - 5 = 555
7x -5 = 555
7x = 560
x = 80
Use PEMDAS above; you are in college so I assume you didn't need a step-by-step.
Now plug in x for each item.
x = grams for hat and x = 80.
5x = grams for sweater and 5(80) = 400
x-5 = grams for scarf and 80 - 5 = 75
Now check. 75 + 400 + 80 = 555? Yes, it does.
So, 75 g for scarf, 80 g for hat, and 400 g for sweater.
I hope this is what you were looking for.
The grams needed for hat, sweater and scarf will be 80, 400 and 75 respectively.
Let grams of wool needed for hat = x
Let grams of wool needed for sweater = 5 × x = 5x
Let grams of wool needed for scarf = x - 5
Therefore, the equation will be:
x + 5x + (x - 5) = 555
x + 5x + x - 5 = 555
Collect like terms
7x = 555 + 5
7x = 560
Divide both side by 7
7x/7 = 560/7
x = 80
Hat requires 80 grams of wool
Grams of wool needed for sweater = 5x = 5 × 80 = 400 grams
Grams of wool needed for scarf = x - 5 = 80 - 5 = 75 grams
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