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Grace and her friend are doing some back-to-school shopping. Grace buys binders and notebooks for total. Her friend spends a total of on binders and notebooks. How much do Grace and her friend spend together on notebooks?____
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Q. Grace and her friend are doing some back-to-school shopping. Grace buys binders and notebooks for total. Her friend spends a total of on binders and notebooks. How much do Grace and her friend spend together on notebooks?____
- Calculate Total Cost: Calculate the total cost of Grace's shopping: binders notebooks .
- Solve Equations: Calculate the total cost of her friend's shopping: binders notebooks $= \$\(21\).\(00\).
- Simplify Second Equation: Assume the cost of one binder and one notebook is the same for both Grace and her friend. Let's denote the cost of one binder as \(b\) and the cost of one notebook as \(n\). We can set up the following equations based on their purchases: \(4b + 7n = 26.50\), \(3b + 6n = 21.00\).
- Substitute and Solve: Solve the equations simultaneously. First, simplify the second equation by dividing all terms by \(3\):\(b + 2n = 7.00\).
- Calculate Notebook Costs: Substitute \(b\) from the second equation into the first equation:\(\newline\)\(4(7 - 2n) + 7n = 26.50\),\(\newline\)\(28 - 8n + 7n = 26.50\),\(\newline\)\(28 - n = 26.50\),\(\newline\)\(n = 1.50\).
- Calculate Notebook Costs: Substitute \(b\) from the second equation into the first equation: \(4(7 - 2n) + 7n = 26.50\), \(28 - 8n + 7n = 26.50\), \(28 - n = 26.50\), \(n = 1.50\). Substitute \(n = 1.50\) back into the equation for \(b\): \(b + 2(1.50) = 7.00\), \(b + 3 = 7.00\), \(b = 4.00\).
- Calculate Notebook Costs: Substitute \(b\) from the second equation into the first equation: \(4(7 - 2n) + 7n = 26.50\), \(28 - 8n + 7n = 26.50\), \(28 - n = 26.50\), \(n = 1.50\). Substitute \(n = 1.50\) back into the equation for \(b\): \(b + 2(1.50) = 7.00\), \(b + 3 = 7.00\), \(b = 4.00\). Calculate the total amount spent on notebooks by Grace and her friend: Grace: \(4(7 - 2n) + 7n = 26.50\)\(0\) notebooks * \(4(7 - 2n) + 7n = 26.50\)\(1\) = \(4(7 - 2n) + 7n = 26.50\)\(2\), Friend: \(4(7 - 2n) + 7n = 26.50\)\(3\) notebooks * \(4(7 - 2n) + 7n = 26.50\)\(1\) = \(4(7 - 2n) + 7n = 26.50\)\(5\), Total = \(4(7 - 2n) + 7n = 26.50\)\(6\).
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