A baker makes apple tarts and apple pies each day. Each tart, $t$, requires 1 apple, and each pie, $p$, requires 8 apples. The baker receives a shipment of 184 apples every day. If the baker makes no more than 40 tarts per day, which system of inequalities can be used to find the possible number of pies and tarts the baker can make?

A. $t \leq 40$
$p \leq 184$

B. $t \leq 40$
$8p \leq 184$

C. $t \leq 40$
$p+8t \leq 184$

D. $t \leq 40$
$8p+t \leq 184

Question

A baker makes apple tarts and apple pies each day. Each tart, $t$, requires 1 apple, and each pie, $p$, requires 8 apples. The baker receives a shipment of 184 apples every day. If the baker makes no more than 40 tarts per day, which system of inequalities can be used to find the possible number of pies and tarts the baker can make? 
 
A. $t \leq 40$ 
 $p \leq 184$ 
 
B. $t \leq 40$ 
 $8p \leq 184$ 
 
C. $t \leq 40$ 
 $p+8t \leq 184$ 
 
D. $t \leq 40$ 
 $8p+t \leq 184

GinnyAnswer · Answer

The number of tarts is limited: t ≤ 40 . 
 The total apples used for tarts and pies cannot exceed 184: t + 8 p ≤ 184 . 
 Combine the inequalities to form the system. 
 The system of inequalities is: t ≤ 40 ; 8 p + t ≤ 184 ​ 
 
 Explanation 
 
 Problem Analysis Let's analyze the problem. We are given that the baker makes tarts ( t ) and pies ( p ). Each tart requires 1 apple, and each pie requires 8 apples. The baker has 184 apples daily and makes no more than 40 tarts. We need to find the system of inequalities that represents these constraints. 
 
 Tart Constraint The number of tarts is limited to 40, so we have the inequality: t ≤ 40 
 
 Apple Constraint The total number of apples used for tarts and pies cannot exceed the daily shipment of 184 apples. This can be expressed as: 1 × t + 8 × p ≤ 184 which simplifies to: t + 8 p ≤ 184 
 
 System of Inequalities Combining these two inequalities, we get the system: t ≤ 40 t + 8 p ≤ 184 This corresponds to the fourth option provided. 
 
 Final Answer Therefore, the correct system of inequalities is: t ≤ 40 8 p + t ≤ 184

Examples 
 Imagine you're planning a bake sale. You know you can't make more than 40 fruit tarts because of limited ingredients. Also, each pie needs 8 times more fruit than a tart, and you only have enough fruit for a total of 184 tarts-worth. This system of inequalities helps you figure out the possible combinations of pies and tarts you can bake without exceeding your resources. Understanding these constraints ensures you don't overspend on ingredients and maximize your profit at the bake sale. It's a practical way to manage resources and plan effectively.

Answer (1)

Related Questions in Mathematics

[Free] Select the correct answer. Which equation is equivalent to the given equation? [tex]$x^2-6 x=8$[/tex] A. [tex]$(x-6)^2=44$[/tex] B. [tex]$(x-3)^2=17$[/tex] C. [tex]$(x-6)^2=20$[/tex] D. [tex]$(x-3)^2=14$[/tex]

[Free] Which phrase best describes the translation from the graph [tex]y=6 x^2[/tex] to the graph of [tex]y=6(x+1)^2[/tex]? A. 6 units left B. 6 units right C. 1 unit left D. 1 unit right

[Free] What expression is equivalent to [tex]$\left(5 z^2+3 z+2\right)^2$[/tex] ? A. [tex]$5 z^4+3 z^2+4$[/tex] B. [tex]$5 z^4+9 z^2+4$[/tex] C. [tex]$25 z^4+30 z^3+19 z^2+12 z+4$[/tex] D. [tex]$25 z^4+30 z^3+29 z^2+12 z+4$[/tex]

[Free] The graph of [tex]y=\frac{5}{4} x+1[/tex] is shown below. The coordinate ([tex]0, y[/tex]) is a solution of the equation. Given the [tex]x[/tex]-value of 0, what is the value of the [tex]y[/tex]-coordinate for the coordinate ([tex]0, y[/tex])? [tex]y=[/tex] [blank]

[Free] If [tex]f(-2)=0[/tex], what are all the factors of the function [tex]f(x)=x^3-2 x^2-68 x-120[/tex]? Use the Remainder Theorem. A. [tex](x+2)(x+60)[/tex] B. [tex](x-2)(x-60)[/tex] C. [tex](x-10)(x+2)(x+6)[/tex] D. [tex](x+10)(x-2)(x-6)[/tex]