{"id":"aqua_rat:c1dd9990910d54de65111be7474f09a3","source_id":"aqua_rat","source_item_id":"c1dd9990910d54de65111be7474f09a3","external_id":null,"program":null,"section":"math","category_code":"PHM","category":"Preparing for Higher Math","subcategory_code":null,"subcategory":null,"form_id":null,"passage_id":null,"position":null,"scored":true,"layout_warning":null,"stem":"Alex and Jacob works at a toy shop that make toys. Alex takes 7 hours to make a toy, and Jacob takes 9 hours to make a toy. During a month, both of them makes 35 toys in total. If both of them have worked for almost similar number of hours how many toys have been prepared by Jacob?","stimulus":"","stimulus_html":null,"stem_html":"<p>Alex and Jacob works at a toy shop that make toys. Alex takes 7 hours to make a toy, and Jacob takes 9 hours to make a toy. During a month, both of them makes 35 toys in total. If both of them have worked for almost similar number of hours how many toys have been prepared by Jacob?</p>","rationale_html":"<p>Lets say Alex has worked for x hrs., and Jacob has worked for y hrs. So, number of toys prepared by Alex is x/7, and Jacob is y/9. Since total number of toys prepared by both of them is 35.</p><p>=&gt; x/7 + y/9 = 35.</p><p>=&gt; 9x + 7y = (35)(63)</p><p>=&gt; 7y = (35)(63) - 9x</p><p>=&gt; y = (5)(63) - (9/7)x</p><p>=&gt; y = 315 - (9/7)x</p><p>=&gt; x is to be a multiple of 7. Also, we need to minimize the difference between x &amp; y. Here are some possible values,</p><p>x = 126, y = 315 - (9/7)126 = 153</p><p>x = 133, y = 315 - (9/7)133 = 144</p><p>x = 140, y = 315 - (9/7)140 = 135</p><p>x = 147, y = 315 - (9/7)147 = 126</p><p>As we can see minimum difference between x and y is when x is 140 hrs. and y is 135 hrs. Thus total toys created by Jacob = y/9 = 135/9 = 15.</p><p>A</p>","correct_answer":["A"],"equiv_key":"62985ce44811f6ed78139fd4","has_media":false,"has_mathml":false,"has_table":false,"section_label":"Mathematics","options":[{"label":"A","content_html":"<p>15</p>","ord":0},{"label":"B","content_html":"<p>16</p>","ord":1},{"label":"C","content_html":"<p>17</p>","ord":2},{"label":"D","content_html":"<p>18</p>","ord":3},{"label":"E","content_html":"<p>19</p>","ord":4}],"passage":null,"attribution":{"source_id":"aqua_rat","source_name":"AQuA-RAT algebra word problems with rationales","rights_holder":"Google DeepMind and the AQuA-RAT contributors","canonical_url":"https://github.com/google-deepmind/AQuA","retrieved_from":"https://raw.githubusercontent.com/google-deepmind/AQuA/master/","attribution":"Algebra word problems from the AQuA-RAT dataset (Ling et al., 2017), published by Google DeepMind under the Apache License 2.0.","disclaimer":"AQuA-RAT items are crowdsourced algebra problems, not ACT questions. They carry five answer choices in the pre-2025 ACT Mathematics style and no ACT reporting category. Useful for drilling Preparing for Higher Math content; not a substitute for a real form.","license":"Apache License 2.0. Crowdsourced by DeepMind and published for free use, including commercially.","redistributable":true,"item_count":508},"equivalents":[]}