A mother earned $8750 from royalties on her cookbook. She set aside 20% of this for a down payment on a new home. The balance will be used for her son's future education. She invests a portion of the money in a bank certificate of deposit (CD account) that earns 4% and the remainder in a savings bond that earns 7%. If the total interest earned after one year is $420, how much money was invested at each rate?

Step-by-step explanation:

The problem statement is not clear regarding which money is invested. We will assume it is the 80% of $8750 that is set aside for future education. That amount is

... 0.80 × $8750 = $7000

If x represents the amount invested at 7%, then the total interest earned is

... (7000 -x)×4% + (x)×7% = 420

... 280 +0.03x = 420

... x = 140/0.03 ≈ 4666.67

$4666.67 was invested at 7%.

$2333.33 was invested at 4%.

is there any photos or whatever?

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

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

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

in δacy and δaby,

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)