Expressions, Equations, and Relationships>Writing Real-World Problems for Two-Step Equations and Inequalities(TEKS.Math.7.10.C)
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Texas 7th Grade Math › Expressions, Equations, and Relationships>Writing Real-World Problems for Two-Step Equations and Inequalities(TEKS.Math.7.10.C)
Which real-world scenario matches the equation $3x + 7 = 22$?
A gym charges 7 dollars per visit plus a 3-dollar membership fee. You paid 22 dollars total. How many visits $x$ did you make?
A phone case costs 3 dollars, and sales tax is 7 dollars. The total is 22 dollars.
A ride costs 3 dollars per mile, plus a 7-dollar pickup fee. The total was 22 dollars. How many miles $x$ did you travel?
You had 3 dollars and then saved 7 dollars each day for $x$ days to reach 22 dollars.
Explanation
The equation $3x + 7 = 22$ means 3 dollars times the number of miles ($x$) plus a flat 7-dollar fee equals a total of 22 dollars. Choice C states exactly that structure: total cost = (3 per mile)$\times x$ + 7, and it equals 22.
Which situation could be represented by the inequality $2y - 5 < 13$?
A craft store charges 2 dollars per yard of ribbon, and you use a 5-dollar coupon. You want to spend less than 13 dollars. How many yards $y$ can you buy?
A concert charges 2 dollars per ticket after a 5-dollar coupon, and you plan to spend at least 13 dollars. How many tickets $y$ can you buy?
A gym charges 5 dollars per visit plus a 2-dollar fee. You want the total to be under 13 dollars. How many visits $y$ can you make?
You save 2 dollars each day for $y$ days and then lose 5 dollars; your savings equal 13 dollars.
Explanation
The inequality $2y - 5 < 13$ translates to (2 dollars per yard)$\times y$ minus a 5-dollar coupon is less than 13 dollars. Choice A matches multiply by $y$, subtract 5, and use "less than 13." Other choices change the operations or the inequality type.
Which scenario matches the inequality $4(a + 2) \ge 20$?
You buy $a$ packs of 4 pencils and add 2 loose pencils; you need at least 20 pencils.
You have 2 packs, each with $a + 4$ pencils; you need at least 20 pencils.
You already have 2 boxes of 4 markers, and you buy $a$ more markers; you need at least 20 markers.
You already have 2 boxes of markers. Each box holds 4 markers. If you buy $a$ more boxes, you will have at least 20 markers in all.
Explanation
The expression $4(a + 2)$ means there are $a + 2$ boxes total and each box has 4 items. The inequality $\ge 20$ means the total must be at least 20. Choice D states: 2 boxes already, plus $a$ more boxes, 4 markers per box, for a total of at least 20 markers.
Which real-world situation is modeled by $5n - 8 = 47$?
You pay an 8-dollar membership fee plus 5 dollars per ticket, and your total is 47 dollars. How many tickets $n$ did you buy?
Each ticket costs 5 dollars. You use an 8-dollar coupon. The amount you pay is 47 dollars. How many tickets $n$ did you buy?
You have 47 dollars, buy tickets that cost 5 dollars each, and have 8 dollars left. How many tickets $n$ did you buy?
Each ticket costs 5 dollars. After using an 8-dollar coupon, your total is less than 47 dollars. How many tickets $n$ did you buy?
Explanation
In $5n - 8 = 47$, the term $5n$ represents 5 dollars per ticket times $n$ tickets, the "$-8$" represents subtracting an 8-dollar coupon, and the result equals 47 dollars. Choice B matches this exactly. The others change the sign, equality, or totals.
Choose the situation that could be represented by $10 - 2t \le 4$.
You have 10 tickets. Each game costs 2 tickets. After playing $t$ games, you will have 4 tickets or fewer left.
You start with 10 tickets and earn 2 tickets per game. After playing $t$ games, you will have at least 4 tickets.
You start with 4 tickets and lose 2 tickets per game. After playing $t$ games, you will have no more than 10 tickets.
You have 10 tickets. Each game costs 2 tickets. After playing $t$ games, you will have more than 4 tickets left.
Explanation
The inequality $10 - 2t \le 4$ says start with 10, subtract 2 for each of $t$ games, and the remaining tickets are at most 4. Choice A states exactly that: 10 minus 2 per game is no more than 4.