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5100176
Anton sells handmade clay mugs at a school fair. Small mugs cost \(\$1.30\) each, and large mugs cost \(\$2.80\) each. He earns \(\$24.40\) in total and sells \(8\) small mugs. How many large mugs does he sell?

Hints

- Find how much Anton earns from the small mugs. - Subtract that amount from the total revenue. - Determine how many large-mug prices fit into the remaining revenue.

Solution

1. Find the revenue from the small mugs: \(8 \times \$1.30 = \$10.40\). 2. Find the revenue from the large mugs: \(\$24.40 - \$10.40 = \$14.00\). 3. Find the number of large mugs: \(\$14.00 \div \$2.80 = 5\).

Answer

Anton sells \(5\) large mugs.
5108906
Find each quotient. In part c), first write the percent as a decimal. a) \(4.8\div0.6\) b) \(1.25\div0.5\) c) \(12\%\div5\)

Hints

- For a decimal divisor, create an equivalent division with a whole-number divisor. - Recall that percent means “per hundred.” - Multiplying both dividend and divisor by the same power of \(10\) does not change the quotient.

Solution

1. For a), multiply both dividend and divisor by \(10\): \(48\div6=8\). 2. For b), multiply both dividend and divisor by \(10\): \(12.5\div5=2.5\). 3. For c), \(12\%=0.12\), and \(0.12\div5=0.024\).

Answer

a) \(8\) b) \(2.5\) c) \(0.024\)
5112286
Evaluate the expression using the order of operations: \(4.5\times0.2-1.2\div0.3\)

Hints

- Which operations must be completed before the subtraction? - When dividing by a decimal, you can multiply both numbers by the same power of \(10\) to make the divisor a whole number. - Think about the sign when subtracting a larger positive number from a smaller one.

Solution

1. Multiply: \(4.5\times0.2=0.9\). 2. Divide: \(1.2\div0.3=4\). 3. Subtract: \(0.9-4=-3.1\).

Answer

\(-3.1\)
5204116
Lucas wants to buy \(6\) small bags of gummy candy at \(\$1.10\) each. At checkout, he finds that he is exactly \(\$1.10\) short. a) How much money does Lucas have? b) What is the greatest number of bags he can buy?

Hints

- Find the cost of all six bags. - Subtract the amount Lucas is short. - Divide his money by the price per bag.

Solution

1. Six bags cost \(6 \times \$1.10 = \$6.60\). 2. Lucas has \(\$6.60 - \$1.10 = \$5.50\). 3. The greatest number he can buy is \(\$5.50 \div \$1.10 = 5\) bags.

Answer

a) Lucas has \(\$5.50\). b) He can buy at most \(5\) bags.
5102706
Find each missing value or compare the results. a) Find \(x\) if \(x\,\text{km}\div40=75\,\text{m}\). b) Find \(x\) if \(0.6\,\text{m}^2\div x=12\,\text{dm}^2\). c) Evaluate \(5\,\text{t}\div200\) in kilograms and \(30\,\text{kg}\div1.2\) in kilograms. What do you notice?

Hints

- Reverse a division equation to find a missing value. - Make the units match on both sides of each equation. - For division by \(1.2\), multiply both numbers by \(10\). - Equal quotients have the same numerical value.

Solution

1. For a), \(75\,\text{m}=0.075\,\text{km}\). From \(x\div40=0.075\), multiply by \(40\): \(x=0.075\times40=3\). 2. For b), \(0.6\,\text{m}^2=60\,\text{dm}^2\). From \(60\div x=12\), \(x=60\div12=5\). 3. For c), \(5\,\text{t}=5000\,\text{kg}\), and \(5000\div200=25\). Also, \(30\div1.2=25\). Both results are \(25\,\text{kg}\).

Answer

a) \(x=3\) b) \(x=5\) c) Both results are \(25\,\text{kg}\).
5142026
One worker bee has a mass of about \(0.1\,\text{g}\). An entire healthy colony has a mass of \(2.1\,\text{kg}\). a) About how many bees are in the colony? b) About \(\frac{1}{3}\) of the bees are foragers. How many forager bees are there? c) Each forager brings back an average of \(0.03\,\text{g}\) of nectar per trip. How many kilograms of nectar do all the foragers collect during one trip each?

Hints

- Express the colony mass and one bee’s mass in the same unit. - Divide the total mass by the mass of one bee to find a count. - Use each previous answer in the next part.

Solution

1. Convert the colony mass: \(2.1\,\text{kg} = 2100\,\text{g}\). 2. Find the number of bees: \(2100\,\text{g} \div 0.1\,\text{g} = 21{,}000\). 3. Find the number of foragers: \(\frac{1}{3} \times 21{,}000 = 7000\). 4. Find the nectar mass: \(7000 \times 0.03\,\text{g} = 210\,\text{g}\). 5. Convert: \(210\,\text{g} = 0.21\,\text{kg}\).

Answer

a) About \(21{,}000\) bees b) About \(7000\) forager bees c) \(0.21\,\text{kg}\) of nectar

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