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On a recent art supply shopping trip, excluding taxes, Mark spent 40% of his total on paints, 25% on canvases, and 35% on brushes. If paints are taxed at 5%, canvases at 3%, and brushes at 7%, then the total tax he paid was what percent of the total amount he spent, excluding taxes?

Explanation	Calculations	Help
$We first create a variable T for the total pre-tax spending.$	$T = total pre-tax spending$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate "40 percent", "25 percent", and "35 percent" of the total pre-tax spending into expressions in terms of T.$	$Paints = \frac{40}{100} T = 0.4 T Canvases = \frac{25}{100} T = 0.25 T Brushes = \frac{35}{100} T = 0.35 T$	Theory & Tactics Method Card TRANS2-A Click to view full details
$We translate "5 percent tax on the paints", "3 percent tax on the canvases", and "7 percent tax on the brushes" into decimal multipliers applied to each category of spending.$	$Tax on paints = 0.05 \times 0.4 T = 0.02 T Tax on canvases = 0.03 \times 0.25 T = 0.0075 T Tax on brushes = 0.07 \times 0.35 T = 0.0245 T$	Theory & Tactics Method Card TRANS2-A Click to view full details
$We add these tax amounts and express the total as a percentage of the pre-tax spending.$	$Total tax = 0.02 T + 0.0075 T + 0.0245 T = 0.052 T \frac{Total tax}{T} \times 100% = 0.052 \times 100% = 5.2%$

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B

On a recent art supply shopping trip, excluding taxes, Mark spent 40% of his total on paints, 25% on canvases, and 35% on brushes. If paints are taxed at 5%, canvases at 3%, and brushes at 7%, then the total tax he paid was what percent of the total amount he spent, excluding taxes?

Explanation	Calculations	Help
$We first create a variable T for the total pre-tax spending.$	$T = total pre-tax spending$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate "40 percent", "25 percent", and "35 percent" of the total pre-tax spending into expressions in terms of T.$	$Paints = \frac{40}{100} T = 0.4 T Canvases = \frac{25}{100} T = 0.25 T Brushes = \frac{35}{100} T = 0.35 T$	Theory & Tactics Method Card TRANS2-A Click to view full details
$We translate "5 percent tax on the paints", "3 percent tax on the canvases", and "7 percent tax on the brushes" into decimal multipliers applied to each category of spending.$	$Tax on paints = 0.05 \times 0.4 T = 0.02 T Tax on canvases = 0.03 \times 0.25 T = 0.0075 T Tax on brushes = 0.07 \times 0.35 T = 0.0245 T$	Theory & Tactics Method Card TRANS2-A Click to view full details
$We add these tax amounts and express the total as a percentage of the pre-tax spending.$	$Total tax = 0.02 T + 0.0075 T + 0.0245 T = 0.052 T \frac{Total tax}{T} \times 100% = 0.052 \times 100% = 5.2%$

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B