A graph shows Frankie's factory information : 50 grams of trail mix have 150 calories, 150 grams of trail mix has 450 calories, 300 grams of trail mix has 900 calories & 500 grams of trail mix has 1,500 calories. If his sister Fiona eats 75 grams of trail mix , how many calories did she eat? If Rico eats trail mix containing 1,000 Calories . How many grams of trail mix does he eat?
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PRE-ALGEBRA HELP PLEASE (:!?
- Thread starter Yasmin L
- Start date
M
Mandielouwho
Guest
Make a table.
50 150
150 450
300 900
500 1500
Now figure up the change in y over the change in x.
y2-y1
--------
x2-x1
450-150=300
150-50= 100
300/100= 3/1= 3
3 is your slope.
Plug in one of your points.
y(150)= m(3)*x(50)+b
3*50=150
150=150 so b=0
Your equation is y=3x.
Plug in 75 for x.
y=3x(75)
y=225. 75 grams contains 225 calories.
Plug in 1000 for y.
1000=3x.
Divide both by 3.
333.3 = x.
333.3 grams contains 1000 calories.
Need anything else, just let me know.
50 150
150 450
300 900
500 1500
Now figure up the change in y over the change in x.
y2-y1
--------
x2-x1
450-150=300
150-50= 100
300/100= 3/1= 3
3 is your slope.
Plug in one of your points.
y(150)= m(3)*x(50)+b
3*50=150
150=150 so b=0
Your equation is y=3x.
Plug in 75 for x.
y=3x(75)
y=225. 75 grams contains 225 calories.
Plug in 1000 for y.
1000=3x.
Divide both by 3.
333.3 = x.
333.3 grams contains 1000 calories.
Need anything else, just let me know.
ok so you put grams over calories
50/150=150/450=300/900=500/1,500
as you can see, all the proportions are equal, and the top one (grams) is always one third of the bottom number (calories)
So you can do this two ways:
1) Since it is an easy problem, you can do mental math. Since you know the calories is 3 times the grams and the grams is one third of the calories you can do mental math:
Fiona---- 75 grams--- since it is one third, multiply by three to get 225 calories
Rico--- 1,000 calories-- since it is 3 times the grams, divide by 3----- 333.33 or 333 1/3 grams
2) Proportions
Pick on of the original given proportions, or since you know they are all equal to 1/3, use 1/3 as your proportion
Fiona- 75 grams --- Since calories is on the bottom and is what you are trying to figure out... put:
1/3=75/x --- cross multiply, you get 1x, or x=75*3----just in case you did not know * is multiplication
x=225 -- so Fiona ate 225 calories
Rico- 1,000 calories--- now x is on the top because we decided to put grams on top
1/3=x/1,000--- cross multiply
1,000=3x
divide both sides by 3
333 1/3=x x= 333 1/3 or 333.33333.....
so Rico ate 333 1/3 grams
Hope it helped!
50/150=150/450=300/900=500/1,500
as you can see, all the proportions are equal, and the top one (grams) is always one third of the bottom number (calories)
So you can do this two ways:
1) Since it is an easy problem, you can do mental math. Since you know the calories is 3 times the grams and the grams is one third of the calories you can do mental math:
Fiona---- 75 grams--- since it is one third, multiply by three to get 225 calories
Rico--- 1,000 calories-- since it is 3 times the grams, divide by 3----- 333.33 or 333 1/3 grams
2) Proportions
Pick on of the original given proportions, or since you know they are all equal to 1/3, use 1/3 as your proportion
Fiona- 75 grams --- Since calories is on the bottom and is what you are trying to figure out... put:
1/3=75/x --- cross multiply, you get 1x, or x=75*3----just in case you did not know * is multiplication
x=225 -- so Fiona ate 225 calories
Rico- 1,000 calories--- now x is on the top because we decided to put grams on top
1/3=x/1,000--- cross multiply
1,000=3x
divide both sides by 3
333 1/3=x x= 333 1/3 or 333.33333.....
so Rico ate 333 1/3 grams
Hope it helped!