Question

one- & two-step equations: apply
try this
research two grocery stores to find prices for the following items. document your findings in the table.

|grocery store #1 price | grocery store #2 price

head of lettuce| |

gallon of milk | |

a dozen eggs | |

a pound of apples| |

frozen pizza | |

answer the following questions:

1. write an expression to find the cost of 2 pounds of apples and 1 head of lettuce from grocery store #1.
2. write an expression to find the cost of 2 pounds of apples and 1 head of lettuce from grocery store #2.
3. if you have $20 to spend, can you buy 3 dozen eggs and a frozen pizza from either store? which one(s)?
4. how many whole gallons of milk can you buy for $14 at each store? remember, you can't buy part of a gallon. write and solve an equation to find your answer.
5. if you have $32 to spend, how many pounds of apples can you buy with a gallon of milk at each store? write and solve an equation to find your answer.
6. write your own problem similar to question 5 and then write and solve the equation showing how you got the answer. write it as a 6th grader.

Answer 1

I don’t have live access to look up current store prices. I can either use sample prices for both stores (below) and finish the problems, or you can tell me the exact prices you found and I’ll use those. I’ll use simple sample prices now so the math is clear — tell me if you want different numbers or real store names.

Prices (sample):
| grocery store #1 | grocery store #2
head of lettuce | $1.50 | $2.00
gallon of milk | $3.00 | $3.50
a dozen eggs | $2.50 | $3.00
a pound of apples | $2.00 | $2.50
frozen pizza | $4.00 | $5.00

Answers:

1) Expression for cost of 2 pounds of apples and 1 head of lettuce from grocery store #1:
Expression: 2*(price per lb apples) + (price of lettuce) = 2(2.00) + 1.50
Calculate: 4.00 + 1.50 = $5.50

2) Expression for cost of 2 pounds of apples and 1 head of lettuce from grocery store #2:
Expression: 2(2.50) + 2.00
Calculate: 5.00 + 2.00 = $7.00

3) If you have $20, can you buy 3 dozen eggs and a frozen pizza from either store? Which one(s)?
Store #1: 3 dozen eggs = 3(2.50) = $7.50; frozen pizza = $4.00; total = $7.50 + $4.00 = $11.50 → Yes.
Store #2: 3 dozen eggs = 3(3.00) = $9.00; frozen pizza = $5.00; total = $9.00 + $5.00 = $14.00 → Yes.
Both stores: yes (both totals are ≤ $20).

4) How many whole gallons of milk can you buy for $14 at each store? (You can’t buy part of a gallon.) Write and solve an equation.
Let x = number of gallons.
Store #1: 3.00x ≤ 14. Solve x = 14 / 3.00 = 4.666... → whole gallons = 4
(Equation form: 3x = 14, x = 14/3, then take the largest whole number ≤ 14/3 → 4.)
Store #2: 3.50x ≤ 14. Solve x = 14 / 3.50 = 4 → whole gallons = 4
(Equation: 3.5x = 14, x = 14/3.5 = 4.)

5) If you have $32 to spend, how many pounds of apples can you buy with a gallon of milk at each store? Write and solve an equation.
Let p = pounds of apples you can buy (you can buy fractional pounds unless told otherwise).

Store #1:
Equation: price_milk + price_apples * p = 32
3.00 + 2.00p = 32
2.00p = 32 − 3.00 = 29.00
p = 29.00 / 2.00 = 14.5 pounds of apples
(If you must buy whole pounds, you can buy 14 pounds.)

Store #2:
3.50 + 2.50p = 32
2.50p = 32 − 3.50 = 28.50
p = 28.50 / 2.50 = 11.4 pounds of apples
(If only whole pounds allowed, you can buy 11 pounds.)

6) My own problem (written like a 6th grader), then equation and solution:
Problem: "I have $20. If I buy one head of lettuce at grocery store #2, how many whole frozen pizzas can I buy with the rest of my money at store #2?"
Equation: Let n = number of frozen pizzas (whole pizzas).
Price of lettuce + price of pizzas = 20 → 2.00 + 5.00n ≤ 20
Solve: 5n ≤ 18 → n ≤ 18/5 = 3.6 → whole pizzas = 3
Answer: You can buy 3 whole frozen pizzas and one head of lettuce with $20 at store #2.

If you want, I can:
- Re-run everything using the exact prices you find from two real stores, or
- Use different sample prices, or
- Convert all answers to cents or show more step-by-step work for a student.