A tip jar at a coffee shop contains three times as many quarters as dollar bills. It has $8.75 in total, and Zach wants to determine the number of quarters and dollar bills the jar. Zach makes two tape diagrams as shown, one with 3 rectangles and one with 1 rectangle. He labels the diagrams with "$8.75.{}^{\prime\prime} quarters $8.75 dollar bills © 2020 StrongMind. Created using GeoGebra. Zach divided 8.75 by 4 to get 2.1875. He rounded down, wrote "2{}^{\prime\prime} on each rectangle, and stated that 6 quarters and 2 dollar bills are in the tip jar That is incorrect. Which strategy correctly solves the problem? Make a table with a column for "dollars," a column for "quarters," and a column for "value." Start with 1 dollar and 3 quarters, and calculate the value. Continue increasing the dollar column by 1 and the quarter column by 3 until the value reaches $8.75. O The jar contains 3 quarters, so multiply $0.25 by 3, then subtract that value from $8.75 to get the number of dollars. The jar contains 3 dollar bills, so subtract $3.00 from $8.75, then divide by $0.25 to get the number of quarters. Make a table with a column for "dollars," a column for "quarters," and a column for "value." Start with 3 dollars and 1 quarter, and calculate the value. Continue increasing the dollar column by 3 and the quarter column by 1 until the value reaches $8.75.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Related questions

Question

A tip jar at a coffee shop contains three times as many quarters as dollar bills. It has $8.75 in total, and Zach wants to determine the number of quarters and dollar bills in
the jar.
Zach makes two tape diagrams as shown, one with 3 rectangles and one with 1 rectangle. He labels the diagrams with "$8.75.{}^{\prime\prime}
quarters
$8.75
dollar bills
© 2020 StrongMind. Created using GeoGebra.
Zach divided 8.75 by 4 to get 2.1875. He rounded down, wrote “2{}^{\prime\prime} on each rectangle, and stated that 6 quarters and 2 dollar bills are in the tip jar.
That is incorrect.
Which strategy correctly solves the problem?
Make a table with a column for "dollars," a column for "quarters," and a column for "value." Start with 1 dollar and 3 quar
rs, and calculate the value. Continue
increasing the dollar column by 1 and the quarter column by 3 until the value reaches $8.75.
The jar contains 3 quarters, so multiply $0.25 by 3, then subtract that value from $8.75 to get the number of dollars.
The jar contains 3 dollar bills, so subtract $3.00 from $8.75, then divide by $0.25 to get the number of quarters.
Make a table with a column for "dollars," a column for "quarters," and a column for "value." Start with 3 dollars and 1 quarter, and calculate the value. Continue
increasing the dollar column by 3 and the quarter column by 1 until the value reaches $8.75.

Expert Solution

Step 1: Given information

$I n t h e t i p J a r : \begin{array}{rcl} N u m b e r o f d o l l a r c o i n s & = & x \\ N u m b e r o f q u a r t e r s c o i n s & = & 3 x \\ t o t a l m o n e y & = & $ 8.75 \end{array} - - - - - - - - - - - - - - - - - - - -$

$Z a c h s t r a t e g y : \begin{array}{rcl} d i v i d e $ 8.75 b y 4 & t h e n r o u n d o f f & = & r o u n d o f f (\frac{8.75}{4}) \\ d i v i d e $ 8.75 b y 4 & t h e n r o u n d o f f & = & 2 \\ N u m b e r o f d o l l a r s c o i n s & = & 2 \\ N u m b e r o f q u a r t e r c o i n s & = & 6 \\ T o t a l m o n e y & = & 2 \times $ 1 + 6 \times $ 0.25 \\ T o t a l m o n e y & = & $ 3.5 (I n c o r r e c t s o l u t i o n) \end{array}$