SAT Math problems (Please explains)?

1. Suzie deposits a sum of money in a bank acount that pays an annual interest of 6%. If Suzie neither deposits nor withdraws any additional money. How many years will it take for the account to grow to more than 3 times the original deposits?


A. 12 B. 15 C. 17 D. 18 E. 19





2. If x varies directly as y, and x=24 when y=2, what is the value of x when y=8?


A. 8 B. 18 C. 28 D. 30 E. 96





3. A woman invests money in two funds that yield an annual total income of $99.60. One fund pays an annual return of 7%, and the other pays a return of 8%. How much is invested in the fund yielding 8% if the total amount invested at the start of the year is $1280.00?





4. If the measures of the angles of an isosceles triangle are 5x, 2x+10, and x+10. What is the degree measure of the largest angle?


A. 20 degrees B. 40 degrees C. 60 degrees D. 80 degrees


E. 100 degrees|||1. Interest, remember the equation A=Pe^rt, where A is the amount, P is the principle (or starting amount), r is the rate, and t is the time. This problem doesn't give a P, so we'll choose something easy - 1. Then the A would be 3. The rate is .06. And the time is t.





3 = e^.06t [take the natural log of both sides]


ln(3) = .06t


ln(3) / .06 = t





ln should be on your calculator, this will give t=18.3. So E.19 is when the account grows to more than 3 times the original deposit.





2. Varies directly means y=kx (where k is a constant) [If the problem had asked varies indirectly, we'd use the equation xy=k.] Plug in the 1st two numbers to solve for k, then get the second.


2=24k, k = 1/12


8 = 1/12 (x)


96 = x








3. This one reads confusing. So we take a deep breath and relax. The amount made on a fund would be the amount in the fund, times the interest. a1*i1 + a2*i2 = 99.60. The amount in the 1st fund, times its interest, plus the amount in the 2nd times its interest is 99.60. The problem also gives us a1 + a2 = 1280.





a1(.07) + a2(.08) = 99.60





a1 = 1280 - a2





(1280-a2)(.07) + a2(.08) = 99.60





89.60-.07a2+.08a2=99.60





.01a2=10





a2=1000








4. What do the sum of the angles of a triangle add up to? 180掳





5x + 2x+10 + x+10 = 180


8x+20 = 180


8x=160


x=20





5x = 5*20 = 100


2x+10 = 50


x+10 = 30





However, you may have written the problem down wrong. An isosceles triangle has 2 equal sides which gives two equal angles. We didn't get two equal angles in this one.|||Q1. If Suzie deposited Rs. 100 in the bank then at compound interest, if the money amounts to 3 times i.e. Rs. 300 in x years then the equation is


100 [1+(6/100)]^x = 300


(106/100)^x = 3


(1.06)^x = 3


So, x = 19


Therefore the answer is E.19





Q2. x/y= constant as they are directly proportional


24/2 = constant


Therefore x/8 also has to be constant


24/2 = x/8


x = 96


Therefore the answer is E.96





Q3. I'm weak at such questions





Q4. 5x + 2x + 10 + x + 10 = 180


Solve it and x=20 degrees


Therefore the largest angle is 5x i.e. 100 degrees


So, answer is E. 100 degrees





Please, please, please give me the best answer vote . I've not got even a single till date.|||A1) E. 19 years


Say you deposit $100, after 1 year, you have $106, take this 106 and multiply by 6% and add to 106, you have $112 after 2 yrs.


$119 after 3yrs, ... $285 after 18yrs, $303 after 19yrs.





A2) E. 96


"x varies directly as y" is the same as saying "x is directly proportional to y", meaning the ratio x:y


24/2 = x/8


x = 8*12


x = 96





A3) $1000 invested at 8%, $280 at 7%


7% * x + 8% * (1280-x) = $99.60


.07x - .08x + 102.40 = 99.60


-0.01x = -2.80


x = 280 invested at 7%


1280 - 280 = 1000 invested at 8%





A4) E. 100 degrees


5x + 2x +10 + x + 10 = 180


8x + 20 = 180


8x = 160


x = 20


Angles are: 5x = 100 deg, 2x+10 = 50 deg, x+10 = 30 deg|||1. Suzie deposits a sum of money in a bank acount that pays an annual interest of 6%. If Suzie neither deposits nor withdraws any additional money. How many years will it take for the account to grow to more than 3 times the original deposits?





Solve (1.06)^n %26gt; 3 (Hint: use logarithms)





2. If x varies directly as y, and x=24 when y=2, what is the value of x when y=8?





Write x = ky, then figure out what k is, given x=24 when y=2





3. A woman invests money in two funds that yield an annual total income of $99.60. One fund pays an annual return of 7%, and the other pays a return of 8%. How much is invested in the fund yielding 8% if the total amount invested at the start of the year is $1280.00?





(a*0.07 + b*0.08) = $99.60 and a+b = 1280, solve for b





4. If the measures of the angles of an isosceles triangle are 5x, 2x+10, and x+10. What is the degree measure of the largest angle?





5x + 2x+10 + x+10 = 180, solve for x, then find the largest angle





There definitely is something wrong here, an isoceles triangle has 2 angles = and the solution to this problem does NOT give 2 equal angles!