AMC 8 · 2010 · #3
Easy mode Grade 6Problem
Picture a bar graph. It shows the price of 5 gallons of gasoline for each of the first ten months of the year.
Look at the tallest bar to find the highest price. Look at the shortest bar to find the lowest price.
By what percent is the highest price more than the lowest price?
Pick an answer.
AMC 8 2010 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
Try it yourself first — the explanation is most useful after you’ve attempted it.
Toolkit + CCSS Solution
Understand
Restated: A bar graph shows the price of $5$ gallons of gasoline for each of the first $10$ months of the year. Reading the bars, the highest price is $\$17$ (Month $1$) and the lowest price is $\$10$ (Month $3$). By what percent does the highest price exceed the lowest price?
Givens: Bar graph of prices for $5$ gallons of gasoline, Months $1$ through $10$; Vertical axis is price in dollars, with gridlines at $0, 5, 10, 15, 20$; Tallest bar (Month $1$) reaches $\$17$; Shortest bar (Month $3$) reaches $\$10$; Answer choices: (A) $50$, (B) $62$, (C) $70$, (D) $89$, (E) $100$ (percent)
Unknowns: The percent by which the highest price exceeds the lowest price
Understand
Restated: A bar graph shows the price of $5$ gallons of gasoline for each of the first $10$ months of the year. Reading the bars, the highest price is $\$17$ (Month $1$) and the lowest price is $\$10$ (Month $3$). By what percent does the highest price exceed the lowest price?
Givens: Bar graph of prices for $5$ gallons of gasoline, Months $1$ through $10$; Vertical axis is price in dollars, with gridlines at $0, 5, 10, 15, 20$; Tallest bar (Month $1$) reaches $\$17$; Shortest bar (Month $3$) reaches $\$10$; Answer choices: (A) $50$, (B) $62$, (C) $70$, (D) $89$, (E) $100$ (percent)
Plan
Primary tool: #5 Look for a Pattern
Secondary: #7 Identify Subproblems
The problem has a simple shape — read two numbers off the graph, then compute a percent increase — so the work splits cleanly into Tool #7 subproblems: (1) extract the maximum and minimum from the bar chart, (2) compute the percent increase using $(\text{high} - \text{low}) / \text{low} \times 100\%$. Tool #5 (Look for a Pattern) is what makes the second step quick: $\$7$ on a base of $\$10$ is the familiar pattern $\tfrac{7}{10} = 0.70 = 70\%$, so no long division is needed.
Execute — Answer: C
3.MD.B.3 Step 1 - Read the extremes off the bar graph.
- Scanning all $10$ bars, Month $1$ is the tallest and reaches the $\$17$ level; Month $3$ is the shortest and reaches exactly the $\$10$ gridline.
💡 Reading a maximum and minimum off a scaled bar graph is the Grade 3 "draw and interpret a scaled bar graph" skill.
4.OA.A.3 Step 2 - Find the difference between the two prices.
- This is the dollar amount by which the high price exceeds the low price.
💡 Subtraction in a multi-step word problem is a Grade 4 operations standard.
6.RP.A.3 Step 3 - Set up the percent-increase ratio.
- "$A$ is more than $B$ by what percent" means we divide the excess by $B$ (the lowest price, our base) and convert to a percentage.
💡 Choosing the lowest price as the base of the percent — not the highest — is the key Grade 6 ratio-reasoning move.
6.RP.A.3 Step 4 - Compute the ratio and convert to a percent.
- The fraction $\tfrac{7}{10}$ is exactly $0.7$, and $0.7 \times 100\% = 70\%$.
💡 Recognizing $\tfrac{7}{10} = 70\%$ without long division is the percent-pattern shortcut from Grade 6.
3.MD.B.3 Read the extremes off the bar graph. Scanning all $10$ bars, Month $1$ is the ta 4.OA.A.3 Find the difference between the two prices. This is the dollar amount by which t 6.RP.A.3 Set up the percent-increase ratio. "$A$ is more than $B$ by what percent" means 6.RP.A.3 Compute the ratio and convert to a percent. The fraction $\tfrac{7}{10}$ is exac Review
Reasonableness: If the high price were double the low price, the increase would be $100\%$; doubling $\$10$ would mean a high of $\$20$. Since $\$17$ is below $\$20$ but well above $\$10$, the answer must be less than $100\%$ but more than $50\%$. That rules out (A) and (E) and leaves (B) $62$, (C) $70$, (D) $89$. Our calculation $\tfrac{7}{10} = 70\%$ lands on (C), which sits in the expected window.
Alternative: Tool #6 (Guess and Check) on the choices: for each choice $p$, the high price would be $\$10 \times (1 + p/100)$. (A) $50\%$ gives $\$15$, (B) $62\%$ gives $\$16.20$, (C) $70\%$ gives $\$17$, (D) $89\%$ gives $\$18.90$, (E) $100\%$ gives $\$20$. Only (C) reproduces the chart value $\$17$.
CCSS standards used (min grade 6)
3.MD.B.3Draw and interpret scaled picture graphs and bar graphs (Reading the tallest bar ($\$17$ in Month $1$) and the shortest bar ($\$10$ in Month $3$) off the bar graph.)4.OA.A.3Solve multistep word problems using the four operations (Subtracting the two prices to find the $\$7$ excess used in the percent-increase formula.)6.RP.A.3Use ratio and rate reasoning to solve real-world and mathematical problems, including percent problems (Setting up and computing the percent increase $(\$17 - \$10) / \$10 \times 100\% = 70\%$, with the lowest price as the base.)
⭐ This AMC 8 problem only needs Grade 6 percent reasoning — divide the gap by the smaller number — that you already know!
⭐ This AMC 8 problem only needs Grade 6 percent reasoning — divide the gap by the smaller number — that you already know!
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