Mrs. Garcia invests a total of $9099 in two savings accounts. One account yields 7.5% simple interest and the other 9% simple interest. She earned a total of $699.84 interest for the year. How much was invested in each account?
+33616 Let p1 be the amount invested in the 7.5% interest account and p2 be that invested in the other.
Then
p1 + p2 = 9099 ...(1)
0.075*p1 + 0.09*p2 = 699.84 ...(2)
Rewrite (1) as p2 = 9099 - p1 ...(3)
Use (3) in (2)
0.075*p1 + 0.09*(9099 - p1) = 699.84
-0.015*p1 + 0.09*9099 = 699.84
-0.015*p1 = 699.84 - 0.09*9099
p1 =-( 699.84 - 0.09*9099)/0.015
$${\mathtt{p1}} = {\mathtt{\,-\,}}{\frac{\left({\mathtt{699.84}}{\mathtt{\,-\,}}{\mathtt{0.09}}{\mathtt{\,\times\,}}{\mathtt{9\,099}}\right)}{{\mathtt{0.015}}}} \Rightarrow {\mathtt{p1}} = {\mathtt{7\,938}}$$
p1 = $7938
Use this in (3)
p2 = 9099 - 7938
p2 = $1161
+33616 Let p1 be the amount invested in the 7.5% interest account and p2 be that invested in the other.
Then
p1 + p2 = 9099 ...(1)
0.075*p1 + 0.09*p2 = 699.84 ...(2)
Rewrite (1) as p2 = 9099 - p1 ...(3)
Use (3) in (2)
0.075*p1 + 0.09*(9099 - p1) = 699.84
-0.015*p1 + 0.09*9099 = 699.84
-0.015*p1 = 699.84 - 0.09*9099
p1 =-( 699.84 - 0.09*9099)/0.015
$${\mathtt{p1}} = {\mathtt{\,-\,}}{\frac{\left({\mathtt{699.84}}{\mathtt{\,-\,}}{\mathtt{0.09}}{\mathtt{\,\times\,}}{\mathtt{9\,099}}\right)}{{\mathtt{0.015}}}} \Rightarrow {\mathtt{p1}} = {\mathtt{7\,938}}$$
p1 = $7938
Use this in (3)
p2 = 9099 - 7938
p2 = $1161
