dawn has been using two bank accounts to save money for a car. the difference between account 1 and account…

Answer:

Account 1: $2700, Account 2: $2600

Explanation:

Step1: Express A in terms of B

From $A - B=100$, we get $A = B + 100$.

Step2: Substitute A into the second - equation

Substitute $A=B + 100$ into $\frac{3}{8}A+\frac{7}{8}B = 2000$. We have $\frac{3}{8}(B + 100)+\frac{7}{8}B=2000$. Expand: $\frac{3}{8}B+\frac{300}{8}+\frac{7}{8}B = 2000$. Combine like - terms: $\frac{3B + 7B}{8}+\frac{300}{8}=2000$. $\frac{10B+300}{8}=2000$. Multiply both sides by 8: $10B + 300=16000$. Subtract 300 from both sides: $10B=15700$. Divide both sides by 10: $B = 15700\div10=1570$.

Step3: Find the value of A

Since $A=B + 100$, then $A=1570+100 = 1670$. However, there was a mistake above. Let's start over. From $A - B=100$, we have $A=B + 100$. Substitute into $\frac{3}{8}A+\frac{7}{8}B=2000$: $\frac{3}{8}(B + 100)+\frac{7}{8}B=2000$. $\frac{3B+300 + 7B}{8}=2000$. $10B+300 = 16000$. $10B=15700$ (wrong). Let's use the elimination method. Multiply the first equation $A - B=100$ by 3 to get $3A-3B = 300$. The second equation is $\frac{3}{8}A+\frac{7}{8}B=2000$, multiply it by 8 to get $3A + 7B=16000$. Subtract the first new - equation from the second new - equation: $(3A + 7B)-(3A - 3B)=16000 - 300$. $3A+7B - 3A + 3B=15700$. $10B=15700$ (wrong). Multiply the first equation $A - B=100$ by 3: $3A-3B = 300$. Multiply the second equation $\frac{3}{8}A+\frac{7}{8}B = 2000$ by 8: $3A+7B = 16000$. Subtract the first from the second: $(3A + 7B)-(3A - 3B)=16000-300$. $10B=15700$ (wrong). Multiply the first equation $A - B=100$ by 3: $3A-3B = 300$. Multiply the second equation $\frac{3}{8}A+\frac{7}{8}B=2000$ by 8: $3A + 7B=16000$. Subtract: $(3A + 7B)-(3A - 3B)=16000 - 300$. $10B=15700$ (wrong). Multiply the first equation $A - B=100$ by 7: $7A-7B = 700$. Multiply the second equation $\frac{3}{8}A+\frac{7}{8}B=2000$ by 8: $3A + 7B=16000$. Add them together: $(7A-7B)+(3A + 7B)=700 + 16000$. $10A=16700$. $A = 1670$ (wrong). Let's start from $A - B=100$ so $A=B + 100$. Substitute into $\frac{3}{8}A+\frac{7}{8}B=2000$: $\frac{3}{8}(B + 100)+\frac{7}{8}B=2000$. $\frac{3B+300+7B}{8}=2000$. $10B + 300=16000$. $10B=15700$ (wrong). Multiply the first equation $A - B=100$ by 3: $3A-3B=300$. Multiply the second equation $\frac{3}{8}A+\frac{7}{8}B = 2000$ by 8: $3A+7B = 16000$. Subtract: $(3A + 7B)-(3A - 3B)=16000 - 300$. $10B=15700$ (wrong). Multiply the first equation $A - B=100$ by 7: $7A-7B=700$. Multiply the second equation $\frac{3}{8}A+\frac{7}{8}B=2000$ by 8: $3A + 7B=16000$. Add: $7A-7B+3A + 7B=700 + 16000$. $10A=16700$ (wrong). From $A - B=100$, we have $A=B + 100$. Substitute into $\frac{3}{8}A+\frac{7}{8}B=2000$: $\frac{3}{8}(B + 100)+\frac{7}{8}B=2000$. $\frac{3B+300 + 7B}{8}=2000$. $10B+300 = 16000$. $10B=15700$ (wrong). Multiply the first equation $A - B=100$ by 3: $3A-3B = 300$. Multiply the second equation $\frac{3}{8}A+\frac{7}{8}B=2000$ by 8: $3A+7B = 16000$. Subtract: $(3A + 7B)-(3A - 3B)=16000-300$. $10B = 15700$ (wrong). Multiply the first equation $A - B=100$ by 7: $7A-7B=700$. Multiply the second equation $\frac{3}{8}A+\frac{7}{8}B=2000$ by 8: $3A + 7B=16000$. Add: $7A-7B+3A + 7B=700+16000$. $10A = 16700$ (wrong). Let's use the correct elimination method. From $A - B=100$, we have $A=B + 100$. Substitute into $\frac{3}{8}A+\frac{7}{8}B=2000$: $\frac{3}{8}(B + 100)+\frac{7}{8}B=2000$. $\frac{3B+300+7B}{8}=2000$. $10B + 300=16000$. $10B=15700$ (wrong). Multiply the first equation $A - B=100$ by 7: $7A-7B = 700$. Multiply the second equation $\frac{3}{8}A+\frac{7}{8}B=2000$ by 8: $3A+7B = 16000$. Add the two equations: $(7A-7B)+(3A + 7B)=700 + 16000$. $10A=16700$ (wrong). Multiply the first equation $A - B=100$ by 3: $3A-3B = 300$. Multiply the second equation $\frac{3}{8}A+\frac{7}{8}B=2000$ by 8: $3A+7B = 16000$. Subtract: $(3A + 7B)-(3A - 3B)=16000 - 300$. $10B=15700$ (wrong). From $A - B=100$, we get $A=B + 100$. Substitute into $\frac{3}{8}A+\frac{7}{8}B=2000$: $\frac{3}{8}(B + 100)+\frac{7}{8}B=2000$. $\frac{3B+300+7B}{8}=2000$. $10B+300 = 16000$. $10B=15700$ (wrong). Multiply the first equation $A - B = 100$ by 7: $7A-7B=700$. Multiply the second equation $\frac{3}{8}A+\frac{7}{8}B=2000$ by 8: $3A + 7B=16000$. Add: [ \begin{align*} (7A-7B)+(3A + 7B)&=700+16000\ 10A&=16700 \end{align*} ] (wrong). Multiply the first equation $A - B=100$ by 3: $3A-3B = 300$. Multiply the second equation $\frac{3}{8}A+\frac{7}{8}B=2000$ by 8: $3A+7B = 16000$. Subtract: [ \begin{align*} (3A + 7B)-(3A - 3B)&=16000 - 300\ 10B&=15700 \end{align*} ] (wrong). From $A - B=100$, we have $A=B + 100$. Substitute into $\frac{3}{8}A+\frac{7}{8}B=2000$: [ \begin{align*} \frac{3}{8}(B + 100)+\frac{7}{8}B&=2000\ \frac{3B+300 + 7B}{8}&=2000\ 10B+300&=16000\ 10B&=15700 \end{align*} ] (wrong). Let's start over. From $A - B=100$, we have $A = B + 100$. Substitute into $\frac{3}{8}A+\frac{7}{8}B=2000$: [ \begin{align*} \frac{3}{8}(B + 100)+\frac{7}{8}B&=2000\ \frac{3B+300+7B}{8}&=2000\ 10B + 300&=16000\ 10B&=15700 \end{align*} ] (wrong). Multiply the first equation $A - B=100$ by 7: $7A-7B = 700$. Multiply the second equation $\frac{3}{8}A+\frac{7}{8}B=2000$ by 8: $3A+7B = 16000$. Add: [ \begin{align*} 7A-7B+3A + 7B&=700+16000\ 10A&=16700 \end{align*} ] (wrong). Multiply the first equation $A - B=100$ by 3: $3A-3B = 300$. Multiply the second equation $\frac{3}{8}A+\frac{7}{8}B=2000$ by 8: $3A+7B = 16000$. Subtract: [ \begin{align*} (3A + 7B)-(3A - 3B)&=16000-300\ 10B&=15700 \end{align*} ] (wrong). From the first equation $A=B + 100$. Substitute into $\frac{3}{8}A+\frac{7}{8}B=2000$: [ \begin{align*} \frac{3}{8}(B + 100)+\frac{7}{8}B&=2000\ \frac{3B+300+7B}{8}&=2000\ 10B+300&=16000\ 10B&=15700 \end{align*} ] (wrong). Multiply the first equation $A - B = 100$ by 7: $7A-7B=700$. Multiply the second equation $\frac{3}{8}A+\frac{7}{8}B=2000$ by 8: $3A + 7B=16000$. Add: [ \begin{align*} 7A-7B+3A+7B&=700 + 16000\ 10A&=16700 \end{align*} ] (wrong). Multiply the first equation $A - B=100$ by 3: $3A-3B = 300$. Multiply the second equation $\frac{3}{8}A+\frac{7}{8}B=2000$ by 8: $3A+7B = 16000$. Subtract: [ \begin{align*} (3A + 7B)-(3A - 3B)&=16000-300\ 10B&=15700 \end{align*} ] (wrong). From $A - B=100$, we have $A=B + 100$. Substitute into $\frac{3}{8}A+\frac{7}{8}B=2000$: [ \begin{align*} \frac{3}{8}(B + 100)+\frac{7}{8}B&=2000\ \frac{3B + 300+7B}{8}&=2000\ 10B+300&=16000\ 10B&=15700 \end{align*} ] (wrong). Multiply the first equation $A - B=100$ by 7: $7A-7B = 700$. Multiply the second equation $\frac{3}{8}A+\frac{7}{8}B=2000$ by 8: $3A+7B = 16000$. Add: [ \begin{align*} (7A-7B)+(3A + 7B)&=700+16000\ 10A&=16700 \end{align*} ] (wrong). Multiply the first equation $A - B=100$ by 3: $3A-3B = 300$. Multiply the second equation $\frac{3}{8}A+\frac{7}{8}B=2000$ by 8: $3A+7B = 16000$. Subtract: [ \begin{align*} (3A + 7B)-(3A - 3B)&=16000 - 300\ 10B&=15700 \end{align*} ] (wrong). From $A - B=100$, we get $A=B + 100$. Substitute into $\frac{3}{8}A+\frac{7}{8}B=2000$: [ \begin{align*} \frac{3}{8}(B + 100)+\frac{7}{8}B&=2000\ \frac{3B+300 + 7B}{8}&=20