course Mth 151
April 25 around 11:00
assignment 28-queryq7.1.18:
first I would need to form the distributive property on both sides which would give me 4x-36=8x+24. then I would add 36 to both sides to get 4x=8x+60. then I would subtract 8x to both sides to get -4x=60. then I would divide both sides by -4 to get x=-15.
*3
q7.1.31:
i would first multiply 21 to both sides to get rid of the fractions. 21 (2r-3)/7+21*3/7=21*(-r/3), which simplifies to 3(2r-3)+9=-7r. The expand on the left using the Distributive Law:
6r-9+9=-7r. -9+9=0; add 7r to both sides:6r+7r=0so
13r=0 and
r=0/13=0.
*3
q7.1.41:
I would first multiply both sides by 100 to avoid having to deal with decimals:
20(14000)+14t=18(14000+t). Divide both sides by the common factor 2: 10(14000)+7t=9(14000+t). Simplify: 140,000+7t=126,000+9t. Add -9 to both sides: 140,000+7t-9t=126,000+9t-9t. Simplify 140,000-2t=126,000. Add -140,000 to both sides: 140,000-2t=126,000-140,000. Simplify: -2t=-14,000. Divide both sides by -2: t=7000.
*2
q7.1.70:
First multiply both sides by 2 and get 2A=(B+b)*h. Next divide both sides by h to get 2A/h=B+b. Then subtract b:
2A/h-b=B.
Thus B=2A/h-b
*2
q7.1.18:
If we have 20 million more on Thursday then if x = number of Saturday viewers in millions, the number of Thursday viewers is x + 20, again in millions.
The total number is 120 million so we have # of Thursday viewers + # of Saturday viewers=120; using our expressions we have (x+20)+x=120 so that 2x+20=120. Adding -20 to both sides we get 2x+20-20=120-20 or 2x=100. Dividing both sides by 2 we get (2x)/2=100/2 so that x=50.
Thus the number of Saturday viewers is 50, representing 50 million, and the number of Thursday viewers is x+20=70, representing 70 million.GE and GM total 13.5 billion; GE .3 billion less than GM. Show how you set up and solved an equation to obtain the profits of both companies.
If GE makes .3 billion less than GM then if x = GM profits in billions we can say that the GE profits are x - .3. Thus we have x + (x-.3) = 13.5. This gives us 2x - .3 = 13.5 so that 2x = 13.5 + .3 = 13.8 and x = 13.8 / 2 = 6.9.
It follows that x - .3 = 6.9 so that x = 6.9-.3 = 6.6. So GM profits are 6.9 billion and GE profits are 6.6 billion
*2
q7.1.40:
If x is the number of gallons of water added, then : After adding 3 gallons we have 3 + x gallons of 3% solution. Originally we had .04 * 3 gallons of the solute, and since we add only water that's what we still have after adding the water. But now the solute is in 3+x gallons of solution and its concentration is 3%. We have the same amount of solute after as before, since all we added was water, so .04 * 3 = .03 * ( 3 + x ). We solve this equation to get x, the number of gallons of water added. We obtain x = 1. The number of gallons added will be exactly 1
*2
q7.1.50:
If x is the number of nickles then we have x quarters and 2x half-dollars. So the amount of money we have is .05 x + .25 x + .5 (2x).This amount is 2.60 so .05 x + .25 x + .5 (2x) = 2.60. Simplifying the left-hand side: .05 x + .25 x + x = 2.60 1.30 x = 2.60 so that x = 2.60 / 1.30 = 2. We have 2 nickles, 2 quarters and 4 half-dollars
*2"
&#Please let me know if you have questions. &#