Answer:
Wyzant
ALGEBRA WORD PROBLEM
Dorian S. asked • 06/28/17
THREE LINEAR EQUATIONS WITH THREE VARIABLES
A chemist has three different acid solutions. The first acid solution contains 15% acid, the second contains 25%,
and the third contains 70%. He wants to use all three solutions to obtain a mixture of 40 liters containing 45%
acid, using 2 times as much of the 70% solution as the 25% solution. How many liters of each solution should be used?
How to set up as three linear equations to find the answer?
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Arthur D. answered • 06/28/17
TUTOR 4.9 (67)
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set up 2 equations
the first equation...
15%*x+25%*y+70%*2y=45%*40
0.15x+0.25y+1.4y=0.45*40
0.15x+1.65y=18
multiply all terms by 100
15x+165y=1800
divide all terms by 15
x+11y=120
the second equation...
x+y+2y=40
x+3y=40
x=40-3y
substitute into the first equation x+11y=120
40-3y+11y=120
40+8y=120
8y=120-40
8y=80
y=80/8
y=10 liters
x+3*10=40
x+30=40
x=40-30
x=10 liters
10 liters of 15%, 10 liters of 25%, and 20 liters of 70%
check:
10*15%=1.5
10*25%=2.5
20*70%=14
1.5+2.5+14=18
18/40=9/20=45/100=45%
45%*40=18
hope it helps
please mark brainliest
Answer:
61.27 cm
Step-by-step explanation:
refer to picture
#2: 4 cans : $2.36 = 13 : $7.67 SCALE FACTOR: $7.67 divided by $2.36 = 3.25
Use the SF to multiply the missing information.
So 4 cans x 3.25 = 13
YOU CAN BUY 13 CANS FOR $7.67
#4: 2 eggs: 1 1/2 cups of eggs : 10 pancakes = : : 35 pancakes
SCALE FACTOR: 35 pancakes divided by 10 pancakes= 3.5
Use the SF to multiply the missing information
So: 2 eggs x 3.5 = 7
7 EGGS WILL BE NEEDED TO MAKE 10 PANCAKES
#6: 54 pounds: 1 acre = pounds: 12.5 acres
SCALE FACTOR: 12.5 divided by 1 acre= 12.5
Use the SF to find out the mussing information
So, 54 pounds x 12.5 = 675 pounds
THE FARMER CAN HARVEST 675 POUNDS WITH 12.5 ACRES OF FIELD
#8: 90 miles: 120 minutes (5 hours) = 225 miles : 300 minutes (5 hours)
SCALE FACTOR: 225 miles divided by 90 miles = 2.5
Use the SF to figure out the missing information
So, 120 minutes multiplied by 2.5 = 300 minutes (5 hours)
IT WILL TAKE 5 HOURS TO DRIVE 225 MILES
Let
C---------> <span>the cost of a pizza
</span>t----------> <span>number of toppings
we know that
</span>$15.74-3t=$14.49-2t
15.74-14.49=3t-2t-------------> t=1.25
the cost of one topping is $1.25
and the cost of one pizza <span>without topping is
</span>15.74-3*1.25--------> $11.99
then
<span>an equation for the cost of a pizza, C, as a function of the number of toppings, t ordered is
</span>C=11.99+1.25t
the answer is
C=11.99+1.25t
Answer:
n = 6
Step-by-step explanation:
