The Sanchez family had dinner at their favorite restaurant. A sales tax was added to their bill. Amy paid the bill with a gift certificate plus .
How much did the family’s dinner cost before tax? Round your answer to the nearest penny.
Hint: Use the equation , 9 ,
where is the price before tax, is the sales tax rate, and is the total price, including tax.

Ask by Vega Garza. in Brazil

Mar 17,2025

Question

The Sanchez family had dinner at their favorite restaurant. A sales tax was added to their bill. Amy paid the bill with a gift certificate plus .
How much did the family’s dinner cost before tax? Round your answer to the nearest penny.
Hint: Use the equation , 9 ,
where is the price before tax, is the sales tax rate, and is the total price, including tax.

Ask by Vega Garza. in Brazil

Mar 17,2025

UpStudy AI · Accepted Answer

Para resolver este problema, vamos usar a equação fornecida $$ P + rP = T $$, onde:
- $$ P $$ é o preço antes do imposto,
- $$ r $$ é a taxa de imposto (9%),
- $$ T $$ é o preço total, incluindo imposto.

Dado que Amy pagou o total com um certificado de $$ \$10 $$ e $$ \$30.60 $$, o total pago é $$ \$10 + \$30.60 = \$40.60 $$.

Agora, vamos substituir os valores conhecidos na equação:
$$ P + 0.09P = 40.60 $$

Simplificando a equação:
$$ 1.09P = 40.60 $$

Para encontrar o preço antes do imposto ($$ P $$), vamos dividir ambos os lados da equação por 1.09:
$$ P = \frac{40.60}{1.09} $$

Agora, vamos calcular o valor de $$ P $$ e redondeá-lo para o centavo mais próximo.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{40.6}{1.09}$$
- step1: Convert the expressions:
  $$\frac{\frac{203}{5}}{\frac{109}{100}}$$
- step2: Multiply by the reciprocal:
  $$\frac{203}{5}\times \frac{100}{109}$$
- step3: Reduce the numbers:
  $$203\times \frac{20}{109}$$
- step4: Multiply:
  $$\frac{203\times 20}{109}$$
- step5: Multiply:
  $$\frac{4060}{109}$$
O preço antes do imposto ($$ P $$) é aproximadamente $$ \$37.25 $$.

Portanto, a resposta correta é $$ \$37.25 $$.
A família gastou $$ \$37.25 $$ antes do imposto.

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