Ryan was 8 when his parents invested $4000 in a certificate of deposit that pays 6%. if ryan leaves the account alone until the investment doubles, how old will he be? (assume that the interest is not compounded.

Ryan was 8 when his parents invested $4000 in a certificate of deposit that pays 6%. If Ryan leaves the account alone until the investment doubles, how old will he be? (Assume that the interest is not compounded.) 

This one has a twist to it in that it tells you that the interest is not compounded. 

They need to earn $8,000 - $4,000 = $4,000 in interest. 

They earn $4,000 X 6% = $240 in interest per year. 

$4,000 / $240 = 16.67 

16.67 + 8 = 24.67 

Ryan will be 24 and 8 months old when the investment doubles. 

2.)Benjamin has $6000 invested in two accounts. One earns 8% interest per year, and the other pays 7.5% interest per year. If his total interest for the year is $472.50, how much is invested at 8%? 

X = the amount invested at 8% 
($6,000 - X) = the amount invested at 7.5% 

So: 

.08X + .075(6,000 - X) = $472.50 

Now solve: 

.08X + 450 -.075X = $472.50, this reduces to 
.005X = $22.50, which finally reduces to 
X = $4,500 
So $6,000 - X = $1,500 

So the answer is: $4,500 is invested at 8% 

Test the result 

$4,500 X 8% = $360.00 
$1,500 X 7.5% = $112.50 

$360.00 + $112.50 = $472.50, and you've proved your answer

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

ac ≅ ab (given)< cax ≅ < bax   (given)ax ≅ ax (common side)

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

ac ≅ ab (given)< cay ≅ < bay (since < cax ≅ < bax is given and xy is the extension of line ax)ay ≅ ay (common side)

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)