Divide all package numbers by 2:
30 / 2 = 15 Rulers
12 / 2 = 6 Colored Penicils
4 / 2 = 2 Glue Sticks
2.
15 + 6 + 2 = 23
First keep in mind that the center is 5 inches...let L and R be the left and right positions of the two flames...
L=h and R=10-1.5h where h is in hours....
The two flames meet when L=R so we can say:
h=10-1.5h add 1.5h to both sides
2.5h=10 divide both sides by 2.5
h=4
So the flames will meet in five hours, using either original equation we can find this position, I'll use L=h..
L=4
So the position of the flames is 4" from the end. The questions ask how far this point is from the center so:
5-4=1"
So the flames meet 1 inch from the center.
Answer:
1. $2.50
2. 120 bagels
Step-by-step explanation:
1. First, we are told that for every twelve bagels, it costs $5
we can use this information to set up the ratio:
Now, for the first question, we have to figure out how much it would cost to buy six bagels. We can use x for the cost since it is unknown as write the ratio:
since the rate of change is constant, we can set these two ratios equal to each other and cross multiply to solve for x.
=
5 * 6 = 12 * x
30 = 12x
x = 2.5
it would cost $2.50 for 6 bagels.
2. For this problem, we can use the same first ratio of:
Now in this problem, the amount of bagels is unknown. we can use y to represent the number of bagels and set up the ratio of
we can make these two ratios equal to each other and cross multiply
=
5 * y = 12 * 50
5y = 600
y = 120
For $50, you can buy 120 bagels
hope this helped!
Let
x = number of liters of the 40% salt solution
y = number of liters of the 20% salt solution
The two amounts (x and y) must combine to 1500 liters, so
x+y = 1500
we can solve for y to get
y = 1500-x
after subtracting x from both sides
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If we have x liters of the 40% salt solution (composed of pure salt plus other stuff) then we have exactly 0.40*x liters of pure salt. Simply multiply the decimal form of the percentage with the amount of solution.
Similarly, if we have y liters of the 20% solution, then we have 0.20*y liters of pure salt
Combined, we have 0.40*x + 0.20*y liters of pure salt all together.
We want 1500 liters of a 28% solution, so we want 1500*0.28 = 420 liters of pure salt
Equate the two expressions (0.40*x + 0.20*y and 420) to get
0.40*x + 0.20*y = 420
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We have the equation 0.40*x + 0.20*y = 420 and we also know that y = 1500-x
Let's use the substitution property now
0.40*x + 0.20*y = 420
0.40*x + 0.20*( y ) = 420
0.40*x + 0.20*( 1500 - x ) = 420 ... note how y is replaced with 1500-x
Now we can solve for x
0.40*x + 0.20*( 1500 - x ) = 420
0.40*x + 0.20*(1500) + 0.20*(-x) = 420
0.40*x + 300 - 0.20x = 420
0.40*x - 0.20x + 300 = 420
0.20x + 300 = 420
0.20x + 300 - 300 = 420 - 300
0.20x = 120
0.20x/0.20 = 120/0.20
x = 600
Now that we know x, use this to find y
y = 1500-x
y = 1500-600 ... plug in x = 600 (ie replace x with 600)
y = 900
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Answers:
We need 600 liters of the 40% solution
We need 900 liters of the 20% solution
If we take 6/15 and want to make 2/a equivalent to it, we first find out what was done to 6 (the numerator) to make it a 2. The 6 was divided by 3. So we do the same for 15.
15/3=5
The 3rd fraction is 2/5.
You use a similar method for the 4th fraction, b/120.
Now, we find out what was done to 15 (the denominator) to make it a 120.
The 15 was multiplied by 8. So we do the same for 6.
6*8=48
The 4th fraction is 48/120.
For the last fraction 16/c, we use 2/5 as one numerator (16) is a multiple of the other (2).
2 was multiplied by 8 to get to 16, so we do the same for 5.
5*8=40
The last fraction is 16/40.
