Expressions, Equations, and Relationships>Writing One-Variable, Two-Step Equations and Inequalities(TEKS.Math.7.10.A)
Help Questions
Texas 7th Grade Math › Expressions, Equations, and Relationships>Writing One-Variable, Two-Step Equations and Inequalities(TEKS.Math.7.10.A)
A music app charges a $10 monthly fee plus $1.25 per song download. Jordan's budget allows at most $35 this month. Let $s$ be the number of songs. What inequality represents this constraint?
$10 + 1.25s \ge 35$
$1.25 + 10s \le 35$
$10 + 1.25s \le 35$
$1.25s = 35$
Explanation
The fixed amount (constant) is $10$ and the rate (coefficient) is $1.25$ per song, so the expression is $10 + 1.25s$. "At most $35" means the total cannot exceed 35, so use $\le$: $10 + 1.25s \le 35$.
A ride service charges a $3 base fare plus $2.20 per mile. The total cost of Mateo's ride was $19.20. Let $m$ be the number of miles. Which equation models this situation?
$3 + 2.20m = 19.20$
$2.20 + 3m = 19.20$
$3 + 2.20m \le 19.20$
$2.20m = 19.20$
Explanation
The fixed amount (constant) is $3$ and the rate (coefficient) is $2.20$ per mile, so the total cost is $3 + 2.20m$. Because the total was exactly $19.20$, use $=$: $3 + 2.20m = 19.20$.
For a school fundraiser, you already have a $50 donation, and you earn $6 for each bracelet you sell. You must raise at least $200 in total. Let $b$ be the number of bracelets. Which inequality represents this requirement?
$50 + 6b \le 200$
$6 + 50b \ge 200$
$6b = 200$
$50 + 6b \ge 200$
Explanation
The fixed amount (constant) is $50$ and the rate (coefficient) is $6$ per bracelet, so the expression is $50 + 6b$. "At least $200" means the total must be $\ge 200$: $50 + 6b \ge 200$.
A bike shop charges a $25 tuning fee plus $18 per hour of labor. Tessa's bill was $97. Let $h$ be the number of hours of labor. Which equation models the bill?
$25h + 18 = 97$
$25 + 18h = 97$
$25 + 18h \le 97$
$18h = 97$
Explanation
The fixed amount (constant) is $25$ and the rate (coefficient) is $18$ per hour, so the total is $25 + 18h$. Because the bill was exactly $97$, use $=$: $25 + 18h = 97$.
A community pool charges a $15 membership fee plus $4 per visit. You can spend no more than $51 this summer. Let $v$ be the number of visits. Which inequality represents this budget constraint?
$15 + 4v \ge 51$
$15v + 4 \le 51$
$15 + 4v \le 51$
$4v = 51$
Explanation
The fixed amount (constant) is $15$ and the rate (coefficient) is $4$ per visit, giving $15 + 4v$. "No more than $51" means the total is $\le 51$: $15 + 4v \le 51$.